Question

If the image of the point $(1,1,1)$ by a plane $(3,-1,5)$ then the equation of the plane is

• A. $x-y+2z=8$
• B. $x-y+2z=16$
• C. $x-y+2z=14$
• D. None of these

Answer 1

The correct option is A $x-y+2z=8$

Let $A=(1,1,1)$ and $A^{\prime }=(3,-1,5)$
So mid point of $A{A}^{\prime }$ is $(2,0,3)$
and direction ratio of $A{A}^{\prime }$ are $2,-2$ and $4$.
Since $A^{\prime }$ is the image of $A$ so equation of plane is given by,
$2(x-2)-2(y-0)+4(z-3)=0$
$\Rightarrow x-y+2z=8$