Question

The foot of perpendicular from point $P(1,3,4)$ to the plane $2x-y+z+3=0$ is

• A. $(-1,4,3)$
• B. $(3,-2,5)$
• C. $(-3,2,5)$
• D. $(1,-4,3)$

Answer 1

Answer: (A)

$(-1,4,3)$

The foot of the perpendicular from the point P(x,y,z) to the plane ax+by+cz+d=0 is given by
$\left(x-\frac{a(ax+by+cz+d)}{a^2+b^2+c^2},y-\frac{b(ax+by+cz+d)}{a^2+b^2+c^2},z-\frac{c(ax+by+cz+d)}{a^2+b^2+c^2}\right)$
Substituting the points we get option A as the correct answer.