Question

The foot of the perpendicular from (0, 2, 3) to the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ is :

• A. (3, 2, –1)
• B. (–2, 3, 4)
• C. (2, –1, 3)
• D. (2, 3, –1)

Answer 1

The correct option is D (2, 3, –1)

$\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}=\lambda$
Let $P(5\lambda -3,2\lambda +1,3\lambda -4)$ be the foot of perpendicular of A(0, 2, 3). Then AP and given line are perpendicular to each other.
$\therefore (5\lambda -3)5+(2\lambda -1)2+(3\lambda -7)3=0$
$\Rightarrow 38\lambda -38=0\Rightarrow \lambda =1$.
Hence, P = (2, 3, –1)