Question

The equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + = 0, is

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is B

Given, equation of plane is passing throug the point (-1, 3, 2)
$\therefore$ A(x+1) + B(y-3) + C(z-2) = 0 ......(i)
Since plane (i) is perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0
So, A + 2B + 3C = 0 and 3A + 3B + C = 0
$\therefore \frac{A}{2-9}=\frac{B}{9-1}=\frac{C}{3-6}=K\Rightarrow A=-7K,B=8K,C=-3K$
Put the values of A, B and C in (i)
we get, 7x - 8y + 3z + 25 = 0, which is the required equation of the plane.