Question

A ray of light passing through the point A$(1,2,3)$, strikes the plane $x+y+z=12$ at B on reflection passes through point C$(3,5,9)$. The coordinates of point B are

• A. $(2,5,5)$
• B. $(-4,6,10)$
• C. $(-7,0,19)$
• D. $(0,-5,17)$

Answer 1

The correct option is C $(-7,0,19)$

Let image of point $A(1,2,3)$ about $x+y+z=12$ be $D(p,q,r)$ then,

$\frac{p-1}{1}=\frac{q-2}{1}=\frac{r-3}{1}=-2\frac{1+2+3-12}{1^2+1^2+1^2}D(p,q,r)=D(5,6,7)$

Line joining $CD$

$\frac{x-5}{2}=\frac{y-6}{1}=\frac{z-7}{-2}=\lambda$

Coordinate of $B(2\lambda +5,\lambda +6,-2\lambda +7)$

This lies on plane $2\lambda +5+\lambda +6-2\lambda +7=12\Rightarrow \lambda =-6$

$B(2\lambda +5,\lambda +6,-2\lambda +7)=B(-7,0,19)$