Question

The reflection of the point 3i + 5j + 7k with respect to the plane $\overline{r}.$ (2i + j + k) = 6 is

• A. 5i + j + 3k
• B. –5i + j – 3k
• C. 5i – j + 3k
• D. –5i + j + 3k

Answer 1

The correct option is D

–5i + j + 3k

$Letreflectionof(3,5,7)w.r.ttheplane2x+y+z–6=0be(\alpha ,\beta ,\gamma )$

We have $\frac{\alpha -3}{2}=\frac{\beta -5}{1}=\frac{\gamma -7}{1}=\frac{-2(6+5+7-6)}{4+1+1}=-4\therefore \alpha =-5,\beta =1,\gamma =3$