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.