## Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.4

Question 1.

Show that the lines \(\frac { x-1 }{ 2 } \) = \(\frac { y-2 }{ 3 } \) = \(\frac { z-3 }{ 4 } \) and \(\frac { x-4 }{ 5 } \) = \(\frac { y-1 }{ 2 } \) = z, intersects. Find their point of intersection.

Solution:

It is clear from above that both lines intersect each other and the coordinates of point of intersection are (-1, -1, -1).

Question 2.

Check, whether following lines intersect or not

Solution:

Question 3.

Find the foot of perpendicular drawn from point (2, 3, 4) to the line \(\frac { 4-x }{ 2 } \) = \(\frac { y }{ 6 } \) =\(\frac { 1-z }{ 3 } \) Also find the perpendicular distance from point to line.

Solution:

The equation of given line is

Question 4.

Find the vector equation of line that passes throguh point (2, 3, 2) and is parallel to the line

Also find the distance between the line.

Solution:

Line Passes through point (2,3,2)

∴ Position vector of the point is