## Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.3

Question 1.

Find the angle between the lines

Solution:

Question 2.

Find the angle between the lines

Solution:

Question 3.

Show that the line passes through the points (1,-1,2) and (3,4,-2) is perpendicular to the line passes through the points (0, 3, 2) and (3, 5, 6).

Solution:

The equation of line passing through points (1,-1,2) and (3, 4,-2) is

Question 4.

Find k, if lines \(\frac { x-1 }{ -3 } \) = \(\frac { y-2 }{ 2k } \) = \(\frac { z-3 }{ 2 } \) and \(\frac { x-1 }{ 3k } \) = \(\frac { y-1 }{ 1 } \) = \(\frac { z-6 }{ -5 } \) are perpendicular to each other.

Solution:

Question 5.

Find the vector equation of a line passing through point (1,2,- 4) and perpendicular to the both lines

Solution:

Question 6.

Find the cartesian equation of a line that passes through point (- 2, 4, -5) and is parallel to

Solution:

Let Sine passing through (x_{1}, y_{1}, z_{1}) whose dc’s are a, b and c is