# RBSE Solutions for Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.1

## Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.1

Question 1.
Find the direction cosines of a line which makes equal angles with the coordinate axis.
Solution:
Let the line makes equal angle 0 with the coordinate axis.
∴ Direction cosines are
l = cos θ, m = cos θ, n = cos θ
but l2 + m2 + n2 = 1

Question 2.
Find the direction of the line joining two points (4, 2, 3) and (4, 5, 7).
Solution:
Let dc’s of line joining two points P(x1,y1,z1) and Q(x2,y2,z2) are

Question 3.
If a line has direction ratios 2, -1, -2 determine its direction cosines.
Solution:
Given : a = 2, b = -1, c = -2
Let dC’s of line are l,m and n.

Question 4.
A vector $$\overrightarrow { r }$$ makes angles of 45°, 60°, 120° with X, Y and Z-axis respectively. If magnitude of $$\overrightarrow { r }$$ is 2 units then find $$\overrightarrow { r }$$
Solution: