Question

Image of line $\frac{x - 2}{3}=\frac{y - 1}{1}=\frac{z - 1}{- 4}$ in the plane $x+y+z=7$ is

• A. $\frac{x - 4}{1}=\frac{y - 3}{1}=\frac{z - 3}{1}$
• B. $\frac{x - 3}{1}=\frac{y - 4}{1}=\frac{z - 3}{1}$
• C. $\frac{x - 4}{3}=\frac{y - 3}{1}=\frac{z - 3}{- 4}$
• D. $\frac{x - 3}{3}=\frac{y - 4}{1}=\frac{z - 3}{- 4}$

Answer 1

Answer: (C)

The line is perpendicular to normal, hence the line is parallel to plane, so the reflected line has the same direction.
Now, image of $\left(2,1 , 1\right)$ in the plane is $\left(\alpha , \beta , \gamma \right)$ say, then
$\frac{\alpha - 2}{1}=\frac{\beta - 1}{1}=\frac{\gamma - 1}{1}=\frac{- 2 \left(4 - 7\right)}{1 + 1 + 1}=2$
So, the point is $\left(4,3 , 3\right)$