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 Chapter Wise Questions |

Chapter | Chapter 10 |

Chapter Name | Vector Algebra |

Number of Questions Solved | 48 |

Category | Kerala Plus Two |

## Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra

**Short Answer Type Questions (Score 3)**

Question 1.

Consider the regular hexagon OABCDE, where represent in magnitude and direction the vectorsrespectively. In terms of

i. Diagonal represents **(2)**

ii. Diagonal represents **(1) **Answer:

Question 2.

Prove that **(3)**

Ans:

Question 3.

Show that the points (1, 2, 3), (4, 0, 4) 1 j and (-2, 4, 2) are collinear. **(3)**

Answer:

Let A (1, 2, 3), B (4, 0, 4), C (-2, 4, 2) be j the points.

= p.v. of B – p.v. of

Thus are parallel and B is a common point. Hence A, B and C are collinear.

Question 4.

Find the position vector of the point which divides the join of and internally in the ratio 3:1:3 **(3)**

Ans:

Question 5.

a. If

**(1)**

b. Find the projection of on **(2)**

Answer:

Question 6.

a. If the vector are perpendicular .Find the value of λ. **(1)**

b. Find the value of **(2)**

Answer:

Question 7.

a. If θ is the angle between any two vectors , then |when θ is equal to…… **(1)**

b. Find the unit vector perpendicular

to both **(2)**

Answer:

Question 8.

The position vectors of A, B, C are (1,1,1)(1,5,-1) and (2,3,5), then find the greatest angle of the triangle ? **(3)**

Answer:

Question 9.

Using vectors, prove that angle in a semi circle is a right angle. **(3)**

Answer:

Question 10.

Prove by vector method that diagonals of a rhombus bisect each other. **(3)**

Answer:

**Long Answer Type Questions**

**(Score 4)**

Question 1.

Let A (1, -2) and B (3,4) be two points in the plane.

1. Write the position vectors of the points A and B. **(1)**

2. Find **(2)**

3. Unit vector in the direction of **(1)**

Answer:

Question 2.

Find a vector of magnitude 12 units perpendicular to the plane containing the vectors ** ** and (4)

Answer:

Question 3.

Consider

i. Find and **(1)**

ii. Find the unit vector in the’ direction **(1)**

iii. Show that and are orthogonal **(2)**

Answer:

Question 4.

i. If a and b are unit vectors inclined at an angle 0, then prove that and **(2)**

ii. If the sum of two unit vectors is a unit vector, prove that the magnitude of their difference is **(2)**

Answer:

Question 5.

i. Show that the area of the parallelogram having diagonals

**(2)**

ii. Find the values of x for which the angle between the vectors

**(2)**

Answer:

Question 6.

a. If A(l,2,4) and,B(2,-l,3) are two points

i. Find **(1)**

ii. Find unit vector along **(1)**

b. Show that the points with position vectors

and are collinear. **(2)**

Answer:

Question 7.

ABCD Is a réctangle with A as the orgin, and are the position vectors of B and D respectively.

i. What is the position vector of C?

**(1)**

ii. If P, Q, R and S are the midpoints of the sides AB, BC, CD and DA respectively, find the position vectors of P, Q, Rand S. **(1)**

iii. Prove that the quadrilateral PQRS is a rhombus. **(2)**

Ans.

Question 8.

Let the vector be given as

**(4)**

Answer:

Question 9.

Using vectors show that the points A (-1,4,-3), B(3,2,-5), C(-3,8,-5) and D (-3,2,1) are coplanar. **(4)**

Answer:

Question 10.

Using vectors, find the value of k such that the points (k,-10,3), (1,-1,3) and (3,5,3) are collinear. **(4)**

Answer:

**Very Long Answer Type Questions (Score 6)**

Question 1.

i. prove that

**(3)**

ii. Show that angle between diagonals of a cube is

**(3)**

Answer:

Question 2.

a. D,E,F are the mid points of the sides of ΔABC. Show that for any point O,

**(3)**

b. Prove that the points whose position vectors are given by

form a right angled triangle. **(3)**

Answer:

a. Since D, E, F are mid points of BC, AC and AB respectively, we have

Question 3.

Consider the points A(0, -2, 1), B(l, – 1, -2) and C(-l, 1, 0) lying in a plane **(2)**

i. Compute and **(2)**

ii. Find **(2)**

iii. Find a unit vector perpendicular to the plane. 2

Answer:

Question 4.

i. Find **(1)**

ii. Find a unit vector perpendicular to both . **(1)**

iii. In the figure D and E are the mid points of AB and AC respectively. Show that and are parallel. **(2)**

Answer:

Question 5.

a. If is a unit vector and

then write the value of **(3)**

b. Find the projection of

where and **(3)**

Answer:

Question 6.

If and ,find the vector such that **(6)**

Answer:

Question 7.

If are three non zero vectors such that .prove that are mutually at right angles and **(6)**

Answer:

Question 8.

a.

b. The position vector of the points P, Q, R and respectively. Prove that P, Q and R are Collinear. **(3)**

Answer:

This shows that the vectors are collinear. But, Q is common point between . Therefore, given points P,Q and Rare collinear.

Question 9.

If the points with position vectors are collinear, find the value of a. **(6)**

Answer:

Let the points be A, B and C respectively. It is given that points A, B, C are collinear.

Question 10.

Let be three vectors of magnitudes 3, 4, and 5 respectively. If each one is perpendicular to the sum of the other two vectors, prove that

**(6)**

Answer:

**Edumate Questions & Answers**

Question 1.

Choose the correct answer from the bracket. The unit vector in the direction of the vector

ii.

Answer:

Question 2.

i. Choose the correct answer from the bracket .The angle between the vectors with magnitude 1 and 2 respective having

ii. If the vectors are coplanar then find the value of k.

Answer:

Question 3.

i. Write two different vectors having same magnitude.

ii. Find the direction cosines of the vetor . Consider two points A and B with position vectors Find the position vector of a point R which divides the line joining A and B in the 2:1 internally

Answer:

Any two different vectors with same magnitude

Question 4.

i. Choose the correct answer from the bracket. A vector makes an angle with a given directed line l, in the anticlockwise direction , then the projection vector of on line l.

a. Zero

b. zero vector

c. unit vector

d.

ii. Find a unit vector perpendicular to. each of the vector and where

Answer:

i. Since a is perpendicular to l, Then the projection of of d is zero.Projection vector is a zero vector

Question 5.

i. Choose the correct answer from the bracket. If a unit vector makes angles with and with and an acute θ with then θ is

ii. Find a unit Vector a

iii. Write down a unit vector in XY plane, making an angle 60 with the positive direction of x-axis

Answer:

Question 6.

i. If are coplaner ,then is……

Answer:

i. 0

Question 7.

i. is equal to…….

ii. find the area of a triangle leaving the points A(2,3,1), B(1,1,2) and C(1,2,1).

Answer:

i. 0

Question 8.

Consider the points A(0,-2.1), B(1,-1,-2)and C(-1,1,0)lying in the plane

1. Compute

2. Find

3. Find a unit vector perpendicular to the plane.

4. Find Cos A

Answer:

Question 9.

let

i. Compute

ii. Are the products obtained are same?

Answer:

Question 10.

Let

i. Find

ii. Find the unit vector along

iii. Prove that and are parallel vector.

Answer:

**NCERT Questions & Answers **

Question 1.

If is any vector , prove that

i. Find the Projection of

ii. Prove that A,B and C are collinear

Answer:

Question 2.

i. If and vector,prove that

ii. If are unit vectors inclined at an angle θ,then prove that

Answer:

Question 3.

If are two equal vectors then write the value of x+y+z

Answer:

Question 4.

If are three such that .

Find the Value of

Answer:

Question 5.

If respectively are position vectors of the points A, B, C and D,

i. Find the angle between the straight lines AB and CD.

ii. Deduce that AB and CD are parallel.

Answer:

Question 6.

Find the area of the parallelogram whose adjacent sides are determined by the vectors

Answer:

Question 7.

Given that .What can you conclude about the vectors ?

Answer:

Question 8.

Let the vector be such that and ,then is a unit vector ,what is the angle between ?

Answer:

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