Question

The foot of the perpendicular drawn from the point $(1,8,4)$ on the line joining the points $(0,-11,4)$ and $(2,-3,1)$ is

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

Answer 1

Answer: (D)

$(4,5,-2)$

Equation of line joining points $(0,-11,4)$ and $(2,-3,1)$
$\frac{x-2}{2}=\frac{y+3}{8}=\frac{z-1}{-3}=\lambda$......1
$DR$'s of $PQ$ are $2\lambda +1,8\lambda -11,-3\lambda -3$
Now $(2\lambda +1)2+(8\lambda -11)8+(-3\lambda -3)(-3)=0$
$77\lambda -77=0\Rightarrow \lambda =1$

Substituting the value of $\lambda$ in equation $1$, we get
$Q$ as $(4,5,-2)$