Question

Let the plane passing through the point $(-1,0,-2)$ and perpendicular to each of the planes $2 x+ y- z=2$ and $x-y-z=3$ be $a x+ b y+ c z+8=0$. Then the value of $a+b+c$ is equal to:

• A. 3
• B. 8
• C. 5
• D. 4

Answer 1

Answer: (D)

Normal of req. plane $(2 \hat{i}+\hat{j}-\hat{k}) \times(\hat{i}-\hat{j}-\hat{k})$ $=-2 \hat{i}+\hat{j}-3 \hat{k}$
Equation of plane
$-2(x+1)+1(y-0)-3(z+2)=0$
$-2 x+y-3 z-8=0$
$2 x-y+3 z+8=0$
$a +b +c=4$