Question

Q is the image of point P(1, -2, 3) with respect to the plane x - y + z = 7. The distance of Q from the origin is

• A. $\sqrt{\frac{70}{3}}$
• B. $\frac{1}{2}\sqrt{\frac{70}{3}}$
  
• C. $\sqrt{\frac{35}{3}}$
  
• D. $\sqrt{\frac{15}{2}}$

Answer 1

The correct option is A $\sqrt{\frac{70}{3}}$


Normal vector is parallel to $\overline{PQ}$

Equation of $PQ\Rightarrow \frac{x_1-1}{1}=\frac{y_1+2}{-1}=\frac{z_1-3}{1}=\lambda$

$\Rightarrow x_1=\lambda +1,y_1=-2-\lambda ,z_1=3+\lambda$
Midpoint of PQ lies on the plane.

$\Rightarrow \lambda =\frac{1}{3}$

$\therefore Q=(\frac{5}{3},-\frac{-8}{3},\frac{11}{3})$

$\therefore$ distance of Q from origin = $\sqrt{\frac{70}{3}}$