Q. 115.0( 2 Votes )
Find the equation of the plane through the line of intersection of the planes 
and 
and which is perpendicular to the plane 
?[CBSE 2013]
Answer :
We know that, the equation of a plane through the line of intersection of the planes
and 
is given by 
So, equation of the plane passing through the line of intersection of the plane 
and 
is given by
[
] + k[
] = 0
.[
+ k[
] – 4 + 5k = 0 …… (1)
We know that two planes perpendicular if
.
Given that plane (1) is perpendicular to the plane
Using (1)and (3) in equation (2),
[
+ k(
)](
= 0
(1 + 2k)(5) + (2 + k)(3) + (3 – k)( – 6) = 0
5 + 10k + 6 + 3k – 18 + 6k = 0
19k – 7 = 0
k = 
Put the value of k in equation (1),
.[
)] – 4 + 5(
) = 0
.[
] – 
.[
] – 
Multiplying by 19,
Equation of required plane is,
33x + 45y + 50z – 41 = 0
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Find the equation of the plane which contains the line of intersection of the planes
and
and whose intercept on the x-axis is equal to that of on y-axis.
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