Question

A plane passes through the point $\left(- 2 , - 2,2\right)$ and contains the line joining the points $\left(1 , - 1,2\right)$ and $\left(1,1 , 1\right).$ Then the image of $\left(- 7,2 , 3\right)$ in the plane is

• A. $\left(1 , - 1,5\right)$
• B. $\left(- 5 , - 4 , - 2\right)$
• C. $\left(- 6 , - 1 , - 3\right)$
• D. $\left(\frac{13}{23} , \frac{7}{23} , \frac{6}{23}\right)$

Answer 1

Answer: (C)

The plane passes through the points $\left(- 2 , - 2,2\right), \, \left(1 , - 1,2\right), \, \left(1,1 , 1\right)$
Its equation is $\begin{vmatrix} x+2 & y+2 & z-2 \\ 3 & 1 & 0 \\ 3 & 3 & -1 \end{vmatrix}=0$
$\Rightarrow x-3y-6z+8=0$
Image of $\left(- 7,2 , 3\right)$ in the plane is
$\frac{x + 7}{1}=\frac{y - 2}{- 3}=\frac{z - 3}{- 6}=-2\left(\frac{- 7 - 6 - 18 + 8}{1 + 9 + 36}\right)$
$\frac{x + 7}{1}=\frac{y - 2}{- 3}=\frac{z - 3}{- 6}=\left(\frac{23}{23}\right)=1$
$x=-6,y=-1,z=-3$