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

Choose the correct option:

1. The distance of the point from the plane measured parallel to the line is-

Solution.

The equation of the straight line passing through the point and parallel to the line is

So, the point lies on the plane

The point on the plane is

So, the required distance is

So, option (c) is correct.

The angle between the line and the plane is –

Solution.

We know that if is the angle between a line and the plane then

Here,

So, option (a) is correct.

The distance between the parallel planes and is-

Solution.

Two parallel planes are given by

So, the distance between (1) and (2) is

Hence, option (c) is correct.

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The equation of the image of the line in the plane is-

Solution.

The equation of the straight line passing through the point and with direction ratios is given by

So, the point lies on the plane

Let be the image of the point

is the midpoint of the line .

So, the image of the given straight line through the point is

Also, the image of the given straight line through the point is

So, option (d) is correct.

##### Read More : Complete S N Dey Solution of Plane (Ex-5A) Chapter with PDF link

5. The coordinates of the foot of perpendicular from to the plane is-

Solution.

The equation of the straight line passing through the point and with direction ratios is given by

So, the point lies on the plane

So, the required point is

So, option (b) is correct.

6. State which of the following statement is true ?

(a) The distance between the line and the plane is units.

(b) Distance between the parallel planes is units.

(c) A vector parallel to the planes and is

(d) The distance of a point from the plane is units.

Explanation.

Applying the rule where we get, the required distance

So, option (a) is correct.

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7. The foot of the perpendicular from the point to the plane is-

Solution.

By question, the equation of the straight line can be written as

Clearly, the point lies on the plane

Hence, the foot of the perpendicular from the point to the given plane is

option (b) is correct.

8. The vector equation of the plane passing through the origin and the line of intersection of the planes and is-

Solution.

The vector equation of the plane passing through the origin and the line of intersection of the planes and is

where is any non-zero finite number.

Since the plane (1) passes through the origin,

So, by (1) we get,

Hence, option (b) is correct .

9. Value of such that the line is perpendicular to normal to the plane is-

Explanation.

By question,

So, option (a) is correct.

10. The angle between and line of intersection of the planes and is-

Solution.

Given planes are where

If is the angle between and , then

So, option (d) is correct.

11. The acute angle between the planes and is-

Explanation.

If be the acute angle between two given planes, then

So, option (b) is correct.

12. The angle between the line and the plane is-

Explanation.

If be the angle between the line and the plane , then

So, option (b) is correct.