## 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 l^{2} + m^{2} + n^{2} = 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(x_{1},y_{1},z_{1}) and Q(x_{2},y_{2},z_{2}) 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: