Question

The image of the point $(3, 2, 1)$ in the plane $2x-y+3z = 7$ is

• A. (1, 2, 3)
• B. (2, 3, 1)
• C. (3, 2, 1)
• D. (2, 1, 3)

Answer 1

Answer: (C)

(3, 2, 1)

Answer 2

We know that image $(x, y, z)$ of a point $(x_1, y_1, z_1)$ in a plane $ax + by + cz + d = 0$ is
$\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} -= \frac{z- z_{1}}{c}$
$= \frac{ -2 ax_{1 } + by_{1} +cz_{1} + d}{a^{2} + b^{2} +c^{2}}$
Here, point is $(3, 2, 1)$ and plane is $2x - y + 3z = 7$.
$\therefore \, \, \frac{x-2}{2} = \frac{y- 2}{-1} = \frac{z - 1}{ 3 }$
$= \frac{-2 2 3 - 2 + 3 1 - 7}{2^{2} + 1^{2} + 3^{2}}$
$\Rightarrow \frac{x-3}{2} = \frac{y -2}{-1} = \frac{z-1}{3} = -20$
$\Rightarrow x = 3 , y =2 ,z =1$