# NCERT Class 12-Mathematics: Chapter –11 Three Dimensional Geometry Part 9

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**Question 18:**

Find the length and the foot of perpendicular from the point to the plane .

**Answer:**

Equation of the given plane is …(i)

So, the equation of line through and parallel to is given by

If this point lies on the given plane, then

**Question 19:**

Find the equations of the line passing through the point and parallel to the planes and .

**Answer:**

**Question 20:**

Find the equation of the plane through the points and , and perpendicular to the plane .

**Answer:**

**Question 21:**

Find the shortest distance between the lines given by

**Answer:**

We have

Also,

Now, shortest distance between two lines is given by

Now,

And

**Question 22:**

Find the equation of the plane which is perpendicular to the plane and which contains the line of intersection of the planes and .

**Answer:**

**Question 23:**

The plane is rotated about its line of intersection with the plane through an angle . Prove that the equation of the plane in its new position is

**Answer:**

Equation of the plane is