{"id":39061,"date":"2023-01-17T10:00:51","date_gmt":"2023-01-17T04:30:51","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=39061"},"modified":"2023-01-18T09:55:37","modified_gmt":"2023-01-18T04:25:37","slug":"plus-two-maths-chapter-wise-questions-answers-chapter-10","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-questions-answers-chapter-10\/","title":{"rendered":"Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra"},"content":{"rendered":"

Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra are part of Plus Two Maths Chapter Wise Questions and Answers<\/a>. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra.<\/p>\n\n\n\n\n\n\n\n\n\n\n
Board<\/strong><\/td>\nSCERT, Kerala<\/td>\n<\/tr>\n
Text Book<\/strong><\/td>\nNCERT Based<\/td>\n<\/tr>\n
Class<\/strong><\/td>\nPlus Two<\/td>\n<\/tr>\n
Subject<\/strong><\/td>\nMaths\u00a0Chapter Wise Questions<\/td>\n<\/tr>\n
Chapter<\/strong><\/td>\nChapter 10<\/td>\n<\/tr>\n
Chapter Name<\/strong><\/td>\nVector Algebra<\/td>\n<\/tr>\n
Number of Questions Solved<\/strong><\/td>\n48<\/td>\n<\/tr>\n
Category<\/strong><\/td>\nKerala\u00a0Plus Two\u00a0<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra<\/h2>\n

Plus Two Maths Vector Algebra Three Mark Questions and Answers<\/h3>\n

Question 1.
\nFind \\(\\bar{a}+\\bar{b}, \\bar{a}-\\bar{b}\\) and \\(\\bar{b}+\\bar{c}\\) using the vectors.
\n\\(\\bar{a}\\) = 3i + 4j + k, \\(\\bar{b}\\) = 2i – 7 j – 3k and \\(\\bar{c}\\) = 2i + 3j – 9k.
\nAnswer:
\n\\(\\bar{a}+\\bar{b}\\) = 3i + 4j + k + 2i – 7j – 3k = 5i – 3j – 2k
\n\\(\\bar{a}-\\bar{b}\\) = 3i + 4j + k – (2i – 7j -3k) = i + 11j + 4k
\n\\(\\bar{b}+\\bar{c}\\) = 2i – 7j -3k + 2i +3j – 9k
\n= 4i – 4j – 12k.<\/p>\n

Question 2.<\/p>\n

    \n
  1. Find the vector passing through the point A( 1, 2, -3) and B(-1, -2, 1).<\/li>\n
  2. Find the direction cosines along with AB.<\/li>\n<\/ol>\n

    Answer:
    \n1. \\(\\overline{A B}\\) = \\(\\overline{O B}\\) – \\(\\overline{O A}\\) = -i – 2j + k – (i + 2j – 3k) = -2i – 4j + 4k.<\/p>\n

    2. Unit Vector
    \n\"Plus
    \nDirection cosines are \\(\\frac{-2}{6}\\), \\(\\frac{-4}{6}\\), \\(\\frac{4}{6}\\).<\/p>\n

    Question 3.
    \nShow that the points A, B and C with position vectors \\(\\bar{a}\\) = 3i – 4j – 4k, \\(\\bar{b}\\) = 2i – j + k and \\(\\bar{c}\\) = i – 3j – 5k respectively from the vertices of a right angled triangle.
    \nAnswer:
    \n\"Plus
    \n41 = 35 + 6 \u21d2 BC2<\/sup> = AB2<\/sup> + CA2<\/sup>
    \nHence right angled triangle.<\/p>\n

    Question 4.
    \nProve that \\([\\bar{a}+\\bar{b} \\bar{b}+\\bar{c} \\bar{c}+\\bar{a}]=2[\\bar{a} \\bar{b} \\bar{c}]\\).
    \nAnswer:
    \nLHS
    \n\"Plus
    \nNote: If \\(\\bar{a}\\), \\(\\bar{b}\\), \\(\\bar{c}\\) are coplanar then so is \\([\\bar{a}+\\bar{b} \\bar{b}+\\bar{c} \\bar{c}+\\bar{a}]\\).<\/p>\n

    Question 5.
    \nConsider the vector \\(\\bar{p}\\) = 2i – j + k. Find two vectors \\(\\bar{q}\\) and \\(\\bar{r}\\) such that \\(\\bar{p}\\), \\(\\bar{q}\\) and \\(\\bar{r}\\) are mutually perpendicular.
    \nAnswer:
    \nFind a vector \\(\\bar{q}\\) such that \\(\\bar{p} \\cdot \\bar{q}\\) = 0, for this use any \\(\\bar{q}\\) whose two components are randomly selected. Let \\(\\bar{q}\\) = 2i + 2j + xk
    \n\\(\\bar{p} \\cdot \\bar{q}\\) = (2i – j + k) . (2i + 2 j + xk) = 0
    \n\u21d2 4 – 2 + x = 0 \u21d2 x = -2
    \n\"Plus
    \n= 6j + 6k.<\/p>\n

    Question 6.
    \n\"Plus
    \nAnswer:
    \n\"Plus
    \n= i(-12 + 7) – j(-9 – 2) + k(-21 – 8)
    \n= -5i + 11j – 29k
    \n\"Plus
    \n= i(63 + 9) – j(-18 + 6) + k(6 – 14)
    \n= 72i + 12 j – 8k.<\/p>\n

    Question 7.
    \nIf \\(\\bar{a}\\) = 3i + j + 2k,
    \n(i) Find the magnitude of \\(\\bar{a}\\). (1)
    \n(ii) If the projection of \\(\\bar{a}\\) on another vector \\(\\bar{b}\\) is \\(\\sqrt{14}\\), which among the following could be \\(\\bar{b}\\) ? (1)
    \n(a) i + j + k
    \n(b) 6i + 2j + 4k
    \n(c) 3i – j + 2k
    \n(d) 2i + 3j + k
    \n(iii) If \\(\\bar{a}\\) makes an angle 60\u00b0 with a vector \\(\\bar{c}\\), find the projection of \\(\\bar{a}\\) on \\(\\bar{c}\\) (1)
    \nAnswer:
    \n\"Plus<\/p>\n

    (ii) Since projection of \\(\\bar{a}\\) on another vector \\(\\bar{b}\\) and magnitude of \\(\\bar{a}\\) is \\(\\sqrt{14}\\), then \\(\\bar{a}\\) and \\(\\bar{b}\\) are parallel, (b) 6i + 2j + 4k.<\/p>\n

    (iii) Projection of \\(\\bar{a}\\) on \\(\\bar{c}\\)
    \n= |\\(\\bar{a}\\)|cos60\u00b0 = \\(\\sqrt{14}\\) \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{\\sqrt{14}}{2}\\).<\/p>\n

    Question 8.
    \n(i) The projection of the vector 2i + 3j + 2k on the vector i + j + k is (1)
    \n\"Plus
    \n(ii) Find the area of a parallelogram whose adjacent sides are the vectors 2i + j + k and 6i – j (2)
    \nAnswer:
    \n\"Plus<\/p>\n

    (ii) Let \\(\\bar{a}\\) = 2i + j + k, \\(\\bar{b}\\) = i – j
    \n\"Plus
    \n= i(0 + 1) – j(0 – 1) + k(-2 – 1 ) = i + j -3k
    \nArea =
    \n\"Plus<\/p>\n

    Question 9.
    \n(i) The angle between the vectors i + j and j + k is (1)
    \n(a) 60\u00b0
    \n(b) 30\u00b0
    \n(c) 45\u00b0
    \n(d) 90\u00b0
    \n\"Plus
    \nAnswer:
    \n(i) (a) 60\u00b0<\/p>\n

    \"Plus<\/p>\n

    Question 10.
    \n\"Plus
    \nAnswer:
    \n\"Plus<\/p>\n

    (ii) Given, \\(\\bar{a}\\) + \\(\\bar{b}\\) + \\(\\bar{a}\\) = \\(\\bar{0}\\), squaring both sides we get
    \n\"Plus<\/p>\n

    Plus Two Maths Vector Algebra Four Mark Questions and Answers<\/h3>\n

    Question 1.
    \nLet A (2, 3), B (1, 4), C (0, -2), and D (x, y) are vertices of a parallelogram ABCD.<\/p>\n

      \n
    1. Write the position vectors A, B, C, and D. (2)<\/li>\n
    2. Find the value of x and y. (2)<\/li>\n<\/ol>\n

      Answer:
      \n1. Position vector of A = 2i + 3 j
      \nPosition vector of B = i + 4j
      \nPosition vector of C = 0i – 2j
      \nPosition vector of D = xi + yj.<\/p>\n

      2. Since ABCD is a parallelogram, then
      \n\"Plus
      \n(1) \u21d2 -i + j = -xi – (y + 2 )j
      \nx = 1, -2 – y = 1 \u21d2 y = -3
      \n\u2234 D is (1, -3).<\/p>\n

      Question 2.
      \nFind the position vector of a point R which divides the line joining the two points P and Q whose vectors i + 2j – k and -i + j + k in the ratio 2:1<\/p>\n

        \n
      1. internally and<\/li>\n
      2. externally.<\/li>\n<\/ol>\n

        Answer:
        \n\\(\\overline{O P}\\) = i + 2j – k, \\(\\overline{O Q}\\) = -i + j + k
        \nLet R be the position vector of the dividing point,
        \n1.
        \n\"Plus<\/p>\n

        2.
        \n\"Plus<\/p>\n

        Question 3.
        \n(i) Choose the correct answer from the bracket. If a unit vector \\(\\widehat{a}\\) makes angles \\(\\frac{\\pi}{4}\\) with i and \\(\\frac{\\pi}{3}\\) with j and acute angle \u03b8 with k. then \u03b8 is
        \n(a) \\(\\frac{\\pi}{6}\\),
        \n(b) \\(\\frac{\\pi}{4}\\),
        \n(c) \\(\\frac{\\pi}{3}\\),
        \n(d) \\(\\frac{\\pi}{2}\\) (1)
        \n(ii) Find a unit vector \\(\\widehat{a}\\) (1)
        \n(iii) Write down a unit vector in XY plane, making an angle 60\u00b0of with the positive direction of x – axis. (2)
        \nAnswer:
        \n(i) (c), Since I = cos\\(\\frac{\\pi}{4}\\) = \\(\\frac{1}{\\sqrt{2}}\\), m = cos\\(\\frac{\\pi}{3}\\) = 1\/2;
        \nn = cos \u03b8
        \nl2<\/sup> + m2<\/sup> + n2<\/sup> = 1
        \nn2<\/sup> = 1 – (\\(\\frac{1}{2}\\))2<\/sup> – (\\(\\frac{1}{\\sqrt{2}}\\))2<\/sup> = 1\/4
        \nn = \\(\\frac{1}{2}\\), cos\u03b8 = 1\/2 , \u03b8 = \\(\\frac{\\pi}{3}\\).<\/p>\n

        (ii)
        \n\"Plus<\/p>\n

        \"Plus<\/p>\n

        Question 4.
        \nLet the vectors \\(\\bar{a}\\), \\(\\bar{b}\\), \\(\\bar{c}\\) denoted the sides of a triangle ABC.
        \n(i) Prove that (2)
        \n\"Plus
        \n(ii) Find the projection of the vector i + 3j + 7k on the vector 7i – j + 8k (2)
        \nAnswer:
        \n\"Plus<\/p>\n

        (ii) Projection of the vector i + 3j + 7k on the vector 7i – j + 8k
        \n\"Plus<\/p>\n

        Question 5.
        \n(i) If \\(\\bar{a}\\) and \\(\\bar{b}\\) are any two vectors, then axb is (1)
        \n(a) a vector on the same plane where \\(\\bar{a}\\) and \\(\\bar{b}\\) lie.
        \n(b) ab cos\u03b8, if \u03b8 is the angle between them.
        \n(c) a vector parallel to both \\(\\bar{a}\\) and \\(\\bar{b}\\).
        \n(d) a vector perpendicular to both \\(\\bar{a}\\) and \\(\\bar{b}\\).
        \n(ii) Let \\(\\bar{a}\\) = 2i + 4j – 5k, \\(\\bar{b}\\) = i + 2j + 3k. Then find a unit vector perpendicular to both \\(\\bar{a}\\) and \\(\\bar{b}\\). (2)
        \n(iii) Find a vector of magnitude 5 in the direction perpendicular to both \\(\\bar{a}\\) and \\(\\bar{b}\\) (1)
        \nAnswer:
        \n(i) (d) a vector perpendicular to both \\(\\bar{a}\\) and \\(\\bar{b}\\).<\/p>\n

        (ii) \\(\\bar{a}\\) = 2i + 4j-5k, \\(\\bar{b}\\) = i + 2j+3k
        \n\"Plus
        \n= i(12 + 10) – j(6 + 5) + k(4 – 4) = 22i – 11j
        \n\"Plus
        \nTherefore unit vector perpendicular to both \\(\\bar{a}\\) and \\(\\bar{b}\\) is
        \n\"Plus<\/p>\n

        (iii) 5 \u00d7 unit vector perpendicular to both \\(\\bar{a}\\) and \\(\\bar{b}\\)
        \n\"Plus<\/p>\n

        Question 6.
        \nConsider a vector that is inclined at an angle 45\u00b0 to x-axis and 60\u00b0 to y-axis<\/p>\n

          \n
        1. Find the dc\u2019s of the vector. (2)<\/li>\n
        2. Find a unit vector in the direction of the above vector. (1)<\/li>\n
        3. Find a vector which is of magnitude 10 units in the direction of the above vector. (1)<\/li>\n<\/ol>\n

          Answer:
          \n1. Let l, m, n are the direction ratios.
          \nGiven that, l = cos 45\u00b0 = \\(\\frac{1}{\\sqrt{2}}\\), m = cos 60\u00b0 = \\(\\frac{1}{2}\\)
          \n\u21d2 l2<\/sup> + m2<\/sup> + n2<\/sup> = 1
          \n\"Plus
          \n\u2234 the dc\u2019s of the vector are \\(\\frac{1}{\\sqrt{2}}\\), \\(\\frac{1}{2}\\), \\(\\frac{1}{2}\\)<\/p>\n

          2. A unit vector in the direction of the above vector is given by li + mj + nk \u21d2 \\(\\frac{1}{\\sqrt{2}}\\)i + \\(\\frac{1}{2}\\)j + \\(\\frac{1}{2}\\)k.<\/p>\n

          3. A vector, which is of magnitude 10 units in the direction of the above vector is given by
          \n\"Plus<\/p>\n

          Question 7.
          \nConsider the point A(2, 1, 1) and B(4, 2, 3)<\/p>\n

            \n
          1. Find the vector \\(\\overline{A B}\\) (1)<\/li>\n
          2. Find the direction cosines of \\(\\overline{A B}\\) (2)<\/li>\n
          3. Find the angle made by \\(\\overline{A B}\\) with the positive direction of x-axis. (1)<\/li>\n<\/ol>\n

            Answer:
            \n1. \\(\\overline{A B}\\) = 2i + j + 2k<\/p>\n

            2. |\\(\\overline{A B}\\)| = \\(\\sqrt{4+1+4}\\) = 3
            \nThe direction cosines are \\(\\frac{2}{3}\\), \\(\\frac{1}{3}\\), \\(\\frac{2}{3}\\).<\/p>\n

            3. cos \u03b1 = \\(\\frac{2}{3}\\) \u21d2 \u03b1 = cos-1<\/sup>(\\(\\frac{2}{3}\\)).<\/p>\n

            Question 8.
            \nIf i + j + k, 2i + 5j, 3i + 2 j – 3k, i – 6j – k respectively are the position vector of points A, B,C and D. Then<\/p>\n

              \n
            1. Find \\(\\overline{A B}\\) and \\(\\overline{C D}\\). (1)<\/li>\n
            2. Find the angle between the vectors \\(\\overline{A B}\\) and \\(\\overline{C D}\\). (2)<\/li>\n
            3. Deduce that \\(\\overline{A B}\\) parallel to \\(\\overline{C D}\\). (1)<\/li>\n<\/ol>\n

              Answer:
              \n1.
              \n\"Plus<\/p>\n

              2.
              \n\"Plus<\/p>\n

              3. Since the angle between \\(\\overline{A B}\\) and \\(\\overline{C D}\\) is \u03c0 they are parallel.<\/p>\n

              Question 9.
              \nLet ABCD be a parallelogram with sides as given in the figure.<\/p>\n

                \n
              1. Find area of the parallelogram. (2)<\/li>\n
              2. Find the distance between the sides AB and DC. (2)<\/li>\n<\/ol>\n

                \"Plus
                \nAnswer:
                \n1. Given;
                \n\\(\\overline{A B}\\) = i – 3j + k and \\(\\overline{A D}\\) = i + j + k
                \n\"Plus<\/p>\n

                2. Let h be the distance between the parallelsides AB and DC. Then ; Area = Base \u00d7 h _____(2)
                \nHere, Base = |\\(\\overline{A B}\\)|
                \n|i – 3j + k| = \\(\\sqrt{1+9+1}=\\sqrt{11}\\)
                \nFrom (1) and (2)
                \n\"Plus<\/p>\n

                Question 10.
                \nConsider \\(\\bar{a}\\) = i + 2j – 3k, \\(\\bar{b}\\) = 3i – j + 2k, \\(\\bar{c}\\) = 11i + 2j<\/p>\n

                  \n
                1. Find \\(\\bar{a}\\) + \\(\\bar{b}\\) and \\(\\bar{a}\\).\\(\\bar{b}\\) (2)<\/li>\n
                2. Find the unit vector in the direction of \\(\\bar{a}\\) + \\(\\bar{b}\\). (1)<\/li>\n
                3. Show that \\(\\bar{a}\\) + \\(\\bar{b}\\) and \\(\\bar{a}\\) – \\(\\bar{b}\\) are orthogonal. (1)<\/li>\n<\/ol>\n

                  Answer:
                  \n\"Plus<\/p>\n

                  (ii) Unit vector in the direction of
                  \n\"Plus<\/p>\n

                  (iii) We have,
                  \n\"Plus
                  \nTherefore, they are orthogonal.<\/p>\n

                  Question 11.
                  \nLet A (1, -1, 4), B ( 2, 1, 2 ) and C (1, -2, -3 )<\/p>\n

                    \n
                  1. Find \\(\\overline{A B}\\). (1)<\/li>\n
                  2. Find the angle between \\(\\overline{A B}\\) and \\(\\overline{A C}\\).(2)<\/li>\n
                  3. Find the area of the parallelogram formed by \\(\\overline{A B}\\) and \\(\\overline{A C}\\) as adjacent sides. (1)<\/li>\n<\/ol>\n

                    Answer:
                    \n1. \\(\\overline{A B}\\) = P.v of B – P.v of A
                    \n= 2 i + j + 2 k – (i – j + 4k) = i + 2 j – 2k<\/p>\n

                    2. \\(\\overline{A C}\\) = P.v of C – P.v of A
                    \n= i – 2 j – 3 k -(i – j + 4k) = – j – 7k
                    \nLet A be the angle between \\(\\overline{A B}\\) and \\(\\overline{A C}\\)
                    \n\"Plus<\/p>\n

                    3.
                    \n\"Plus
                    \nArea of the parallelogram
                    \n\"Plus<\/p>\n

                    Plus Two Maths Vector Algebra Six Mark Questions and Answers<\/h3>\n

                    Question 1.
                    \nUsing this figure answer the following questions.
                    \n\"Plus<\/p>\n

                      \n
                    1. Find \\(\\overline{O A}\\), \\(\\overline{O B}\\), \\(\\overline{O C}\\) (2)<\/li>\n
                    2. Find \\(\\overline{O D}\\) (2)<\/li>\n
                    3. Find the coordinate of the vertex D. (2)<\/li>\n<\/ol>\n

                      Answer:
                      \n1. \\(\\overline{O A}\\) = (3 – 1)i + (-1 – 2)j + (7 – 3)k = 2i – 3j + 4k
                      \n\\(\\overline{O B}\\) = (2 – 1)i + (4 – 2)j +(2 – 3)k = i + 2j – k
                      \n\\(\\overline{O C}\\) = (4 – 1)i + (1 – 2 )j + (5 – 3 )k = 3i – j + 2 k.<\/p>\n

                      2. From the figure,
                      \n\"Plus<\/p>\n

                      3. Let the vertex of D be (x , y , z),
                      \nThen, \\(\\overline{O D}\\) = (x – 1)i + (y – 2)j + (z – 3)k.
                      \nBut we have,
                      \n\\(\\overline{O D}\\) = 6i – 2j + 5k = (x – 1)i + (y – 2)j +(z – 3)k
                      \nx – 1 = 6 \u21d2 x = 7, y – 2 = -2 \u21d2 y = 0, z – 3 = 5 \u21d2 z = 8.<\/p>\n

                      Question 2.
                      \nOABCDEFG is a cube with edges of length 8 units and axes as shown. L, M, N are midpoints of the edges FG, GD, GB respectively.
                      \n\"Plus<\/p>\n

                        \n
                      1. Find p.v\u2019s of F, B,D and G. (1)<\/li>\n
                      2. Show that the angle between the main diagonals is \u03b8 = cos-1<\/sup>\\(\\left(\\frac{1}{3}\\right)\\). (2)<\/li>\n
                      3. Find the p.v\u2019s of L, M, N. (1)<\/li>\n
                      4. Show that \\(\\overline{L M}+\\overline{M N}+\\overline{N L}=0\\). (1)<\/li>\n<\/ol>\n

                        Answer:
                        \n1. \\(\\overline{O F}\\) = 8 j + 8k, \\(\\overline{O B}\\) = 8i + 8k, \\(\\overline{O D}\\) = 8i + 8k, \\(\\overline{O G}\\) = 8i + 8j + 8k.<\/p>\n

                        2. Consider the main diagonals \\(\\overline{O G}\\) and \\(\\overline{E B}\\)
                        \n\"Plus<\/p>\n

                        3. P.V of L = \\(\\overline{O L}\\) = 4i + 8j + 8k
                        \nP.V of M = \\(\\overline{O M}\\) = 8i + 8j + 4k
                        \nP.V of N = \\(\\overline{O N}\\) = 8i + 4j + 8k<\/p>\n

                        4.
                        \n\"Plus<\/p>\n

                        Question 3.
                        \nUsing the figure answer the following questions
                        \n\"Plus<\/p>\n

                          \n
                        1. Evaluate \\(\\overline{A B}\\).\\(\\overline{A C}\\) (2)<\/li>\n
                        2. Find \\(\\overline{A D}\\) . (2)<\/li>\n
                        3. Find the coordinates of D.<\/li>\n<\/ol>\n

                          Answer:
                          \n1. \\(\\overline{A B}\\) = p.v of B – p.v of A= -4i + 0j + 3k
                          \n\\(\\overline{A C}\\) = p.v of C – p.v of A = 0i – 4 j + 4k
                          \n\\(\\overline{A B}\\).\\(\\overline{A C}\\) = -4 \u00d7 0 + 0 \u00d7 -4 + 3 \u00d7 4 = 12<\/p>\n

                          2.
                          \n\"Plus<\/p>\n

                          3. Let the coordinate of D be (x, y ,z)
                          \n\u21d2 \\(\\overline{A D}\\) = (x – 3)i + (y – 2)j + (z – 1)k,
                          \n\"Plus<\/p>\n

                          Question 4.
                          \nConsider the Parallelogram ABCD
                          \n\"Plus<\/p>\n

                            \n
                          1. Find \\(\\overline{A B}\\) and \\(\\overline{A D}\\) (1)<\/li>\n
                          2. Find the area of the parallelogram ABCD. (1)<\/li>\n
                          3. Find \\(\\overline{A C}\\). (2)<\/li>\n
                          4. Find co-ordinate of C. (2)<\/li>\n<\/ol>\n

                            Answer:
                            \n1. \\(\\overline{A B}\\) = p.v of B – p. v of A
                            \n= 3i + 5j + 8k – (i + 2j + k) = 2i + 3j + 7k
                            \n\\(\\overline{A D}\\) = p.v of D – p. v of A
                            \n= i + 3j + 2k – (i + 2j + k)= 0i + j + k.<\/p>\n

                            2.
                            \n\"Plus<\/p>\n

                            3. By triangle inequality;
                            \n\"Plus<\/p>\n

                            4. Let the co-ordinate of C be (x, y, z)
                            \nThen, \\(\\overline{A C}\\) = (x – 1)i + (y – 2)j + (z – 1)k = 2i + 4j + 8k
                            \nx – 1 = 2 \u21d2 x = 3, y – 2 = 4 \u21d2 y = 6,
                            \nz – 1 = 8 \u21d2 z = 9
                            \nCo-ordinate of C is (3, 6, 9).<\/p>\n

                            Question 5.
                            \nConsider the following quadrilateral ABCD in which P, Q, R, S are the midpoints of the sides.
                            \n\"Plus<\/p>\n

                              \n
                            1. Find \\(\\overline{P Q}\\) and \\(\\overline{S R}\\) in terms of \\(\\overline{A C}\\) (2)<\/li>\n
                            2. Show that PQRS is a parallelogram. (2)<\/li>\n
                            3. If \\(\\bar{a}\\) is any vector, prove that (2)<\/li>\n<\/ol>\n

                              \"Plus
                              \nAnswer:
                              \n1. Using triangle law of addition, we get
                              \n\"Plus<\/p>\n

                              2. From the above explanation we have,
                              \n\"Plus
                              \nand parallel. Similarly, |\\(\\overline{S P}\\)| = |\\(\\overline{R Q}\\)|
                              \nTherefore, PQRS is a parallelogram.<\/p>\n

                              3. Let \\(\\bar{a}\\) = a1<\/sub> i + a2<\/sub> j + a3<\/sub> k
                              \n\"Plus<\/p>\n

                              We hope the given Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra will help you. If you have any query regarding Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

                              Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra are part of Plus Two Maths Chapter Wise Questions and Answers. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra. Board SCERT, Kerala Text Book NCERT Based Class Plus Two Subject Maths\u00a0Chapter Wise Questions Chapter Chapter […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[42728],"tags":[],"yoast_head":"\nPlus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-questions-answers-chapter-10\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra\" \/>\n<meta property=\"og:description\" content=\"Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra are part of Plus Two Maths Chapter Wise Questions and Answers. 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