# NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 8

Doorsteptutor material for UGC Public-Administration is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

**Question 13:**

If a variable line in two adjacent positions has direction cosines *l* and , show that the small angle between the two positions is given by

**Answer:**

We have as direction cosines of a variable line in two different positions.

And

Now,

**Question 14:**

is the origin and is .Find the direction cosines of the line and the equation of plane through at right angle to .

**Answer:**

**Question 15:**

Two systems of rectangular axis have the same origin. If a plane cuts them at distances and , respectively, from the origin, prove that

**Answer:**

Consider are two system of rectangular axes.

Let their corresponding equation of plane be

And

Also, the length of perpendicular from origin to Eq. (i) and (ii) must be same.

## Long Answer (L.A)

**Question 16:**

Find the foot of perpendicular from the point to the line . Also, find the perpendicular distance from the given point to the line.

**Answer:**

**Question 17:**

Find the distance of a point from the line

**Answer:**

We have equation of the line as

Let the coordinates of L be , then Dr’s of PL are .

Also, the direction ratios of given line are proportional to

Since, PL is perpendicular to the given line.

So, the coordinates of L are