Question

The sum of the intercepts on the coordinate axes of the plane passing through the point $(–2,–2,2)$ and containing the line joining the points $(1,–1,2)$ and $(1,1,1)$, is :

• A. $4$
• B. $12$
• C. $-8$
• D. $-4$

Answer 1

The correct option is D $-4$

As three points are given, so equation of the plane is

$\left|\begin{array}{ccc}x+2& y+2& z-2\\ -3& -1& 0\\ -3& -3& 1\end{array}\right|=0$
$\Rightarrow –(x+2)+3(y+2)+6(z–2)=0\Rightarrow x-3y-6z+8=0\text{In intercept form}\Rightarrow \frac{x}{-8}+\frac{y}{\frac{8}{3}}+\frac{z}{\frac{8}{6}}=1$
sum of intercepts $=-8+\frac{8}{3}+\frac{8}{6}=-4$