##### In the previous article , we have solved complete MCQ 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).

1. Find the angle between the line and the plane

Solution.

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

Here,

By (1), we get

2. Obtain the equation of the plane passing through the point and perpendicular to the planes and [CBSE-’09]

Solution.

Let the direction ratios of the normal to the plane (to be determined) be

So, from (1) and (2) we get by cross-multiplication,

Since the plane passes through the point and perpendicular to the given planes , the equation of the plane can be written as

3. Find the equation of the plane passing through the points and and which is perpendicular to the plane

Solution.

The equation of the plane passing through the point can be written as

Since the plane (1) passes through the point

Again, since the plane (1) is perpendicular to the plane so

From and , we get by cross-multiplication,

Hence, using (1) and (4) we get the equation of the plane as follows :

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4. Find the equation of the plane passing through the intersection of the planes and the point

Solution.

Given planes are

The equation of the plane passing through the planes (1) and (2), can be written as

The plane (3) passes through the point The position vector of the point can be written as

Now, we calculate the following values :

Hence from (3) we get the required equation of the plane (after substituting the aforesaid values) as follows :

5. Find the equation of a plane passing through the points and and parallel to the line

Solution.

The equation of the plane through the point is

Since the plane (1) passes through the point

Again the plane (1) is parallel to the straight line

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

So, by using (1) and (4), we get the required equation of the plane

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

Solution.

The given equations of planes are

The equation of the plane through the planes (2) and (3) is

Since the plane (4) is perpendicular to the plane (1),

Now, we calculate the following values.

Hence, from (4) we get the required equation of the plane (after substituting the aforesaid values) as follows :

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7. Find the equation of the plane through the line of intersection of the planes and and perpendicular to

Solution.

The given equations of planes are

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

Since the plane (1) is perpendicular to the plane

Now, we calculate the following values .

Hence, from (3) we get the required equation of the plane (after substituting the aforesaid values) as follows :