Question

The equations of the plane which passes through $(0,0,0)$ and which is equally inclined to the planes $x-y+z-3=0$ and $x+y+z+4=0$ is/are-

• A. $y=0$
• B. $x=0$
• C. $x+y=0$
• D. $x+z=0$

Answer 1

Answer: (A), (D)

$y=0$
$x+z=0$

The equations of the plane which is equally inclined to the planes $x-y+z-3=0$ and $x+y+z+4=0$ is/are-
$\frac{x-y+z-3}{\sqrt{1^2+1^2+1^2}}\pm \frac{x+y+z+4}{\sqrt{1^2+1^2+1^2}}=0$
$\Rightarrow x+z=-1$ and $y=\frac{-7}{2}$
If the plane contains origin
Then desired planes are $x+z=0$ & $y=0$
Ans: A,D