# NCERT Class 12-Mathematics: Chapter – 11 Three Dimensional Geometry Part 9 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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