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:

RBSE Solutions for Class 12 Maths