Question

A plane which bisects the angle between the two given planes $2x–y+2z–4=0$ and $x+2y+2z–2=0,$ passes through the point :

• A. $(1,-4,1)$
• B. $(2,4,1)$
• C. $(2,-4,1)$
• D. $(1,4,-1)$

Answer 1

The correct option is C $(2,-4,1)$

Equation of angle bisectors are
$\frac{2x-y+2z-4}{\sqrt{2^2+(-1{)}^2+2^2}}=\pm \frac{x+2y+2z-2}{\sqrt{1^2+(2{)}^2+2^2}}$

Taking positive sign, we get
$x–3y–2=0...\left(1\right)$
Taking negative sign, we get
$3x+y+4z–6=0...\left(2\right)$

Now by putting all the given options in the equation $\left(1\right)$ and $\left(2\right)$, we find that
$(2,-4,1)$ satisfies the equation $\left(2\right)$