## Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 12 Introduction to Three Dimensional Geometry

Question 1.

Consider a point A(4,8,10) in space.

a. Find the distance of the point A from XY- plane.

b. Find the distance of the point A from X – axis.

c. Find the ratio in which the line segment joining the point A and B (6,10, -8) is divided by YZ -plane.

[March-2018]

Answer:

a. 10 [Z coordinate of the point]

Let P(4,0,0) be a line on the X-axis.

Question 2.

a. The distance between the points (1, -2,3) and (4,1,2) is

i.

ii.

iii.

iv.

b. The centroid of a triangle ABC is at the point (1, 2, 3). If the coordinates of A and B are (3, -5, 7)

and (-1, 7, -6) respectively. Find the coordinates of the point C. [March-2017]

Answer:

Question 3.

a. Which one of the following points lies in the sixth octant?

i. (-4,2,-5)

ii.(-4,-2,-5)

iii. (4,-2,-5)

iv. (4,2,5)

b. Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2,4,7)

and (3, -5,8). [March-2016]

Answer:

a.i. (-4, 2, -5)

Let YZ plane divides the line joining the points A (-2, 4, 7) and B (3, -5, 8) at R (x, y, z) in the ratio k: 1.

Then x coordinates of R = 0.

Question 4.

a. A point in the XZ plane is………………

i. (1,1,1)

ii. (2,0,3)

iii. (2,3,0)

iv. (-1,2,3)

b. Show that the points A (1, 2, 3), B (-1, -2,-1), C (2,3,2) and D (4,7,6) are the vertices of a parallelogram. [March-2015]

Answer:

a. (2,0,3)

Question 5.

a. Find the distance between the points (2,3,5) and (4,3,1).

b. Find the ratio in which the line segment joining the points A (4, 8, 10) and B (6,10,-8) 9s divided by the XY plane.[March-2014]

Answer:

Question 6.

a. Find the distance between the points (2,-1,3) and (-2,1,3).

b. Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) internally in the ratio of 2:3. [March-2013]

Answer:

Question 7.

Given three points A(-4,6,10), B (2,4,6) and C (14,0,2).

i. Find AB,BC and AC.

ii. Prove that A, B and C are nonlinear. [February-2013]

Answer:

Question 8.

If is the centroid of ΔPQR

with vertices P (a, 7, -10), Q (1, 2b, -6), R (4,9,3c) find the values of a, b, and c.

b. Prove that A PQR is isosceles. [March-2012]

Answer:

Question 9.

Consider the points A (-2,3,5), B (1,2,3) and C (7,0,-1).

i. Using the distance formula, show that the points A, B and C are collinear.

ii. Find the ratio in which B divides the line segment AC. [March-2011]

Ans:

Question 10.

Consider the points A (-2, 4, 7) and B (3,-5,8).

i. If P divides AB in the ratio k: 1, then find the coordinates of P.

ii. Find the co-ordinates of the point where the line segment AB crosses the YZ-plane. [August-2009]

Answer:

i. Section formulae,

Question 11.

Consider the points A (2,1,3) and B (1,2,1).

a. Find the ratio in which the join of AB is divided by YZ plane.

b. Also find the point of division. [March-2009]

Answer:

a. Any point on the YZ plane is (0, y, z) Let this point divides the line joining (2,1,3) and B (1,2,1) in the ratio m: n