# Plane | Part-3 | Ex-5B

##### In the previous article , we have solved few VSA type questions of Plane Chapter (Ex-2B) of S N De Mathematics(Chhaya). In the following article, we are going to discuss/solve VSA (Very Short Answer) Type Questions of S.N.Dey Mathematics-Class 12 of the chapter Plane (Ex-5B).

8. Find the distance of the point from the point of intersection of the line   and the plane [NCERT]

Solution.

Let the position vector of the point of intersection be

This point lies on the plane

The position vector of the point of intersection is i.e.

So, the distance between the points and is

9. Find the value of such that the line is perpendicular to the plane

Solution.

The given straight line is and the plane is

Since the straight line (1) is perpendicular to the plane (2),

10.  Find the distance of the point with position vector from the plane

Solution.

The distance of the point from the given plane

11. Find the distance between the parallel planes and

Solution.

The given planes are and

Clearly, the planes (1) and (2) are parallel to each other.

So, the distance between them is

12. If the line is parallel to the plane , find the value of

Solution.

The given straight line is and the given plane is

Since the straight line (1) is parallel to the plane (2), so

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

Solution.

The equation of the plane which contains the line of intersection of planes (1) and (2) is

The plane (3) is perpendicular to the plane

Now, we calculate the following values in (3).

Hence, from (3) we get,

So, equation (4) represents the vector equation of the required plane.

14. Find the equation of the plane passing through the points and and parallel to the line   [CBSE ]

Solution.

The equation of the plane passing through the point is

Since the plane (1) is passing through the point

Since the plane is parallel to the given straight line

From (2) and (3) we get by cross-multiplication,

The required equation of the plane is

15. Find the coordinates of the point where the line through the points and crosses the xy-plane.

Solution.

The equation of the any straight line through the points and can be written as

So, any point on the straight line (1) can be written as

If this straight line crosses the xy-plane, then as on the xy-plane

The co-ordinates of the point where the line crosses the xy-plane is