# Plane | Part-2 | Ex-5B

##### 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 : Master NEET (UG) Biology with New Pattern Matching, Assertion Reason (AR), 2 Statement & Multiple Statement Questions (MSQs) 2nd Edition Paperback

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 : Quickly Memorise Biology for NEET AIIMS NTA I NCERT based I Class 11 and 12 I Ktricks I Dr Kunal Tatte Paperback

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 : 