Question

The coordinates of the foot of the perpendicular drawn from the point $A(1,0,3)$ to the join of the points $B(4,7,1)$ and $C(3,5,3)$ are

• A. $(5,7,17)$
• B. $(\frac{-5}{7},\frac{7}{3},\frac{-17}{3})$
• C. $(\frac{5}{7},\frac{-7}{3},\frac{17}{3})$
• D. $(\frac{5}{7},\frac{7}{3},\frac{17}{3})$

Answer 1

The correct option is D $(\frac{5}{7},\frac{7}{3},\frac{17}{3})$

The cartesian equation of the line passing through given 2-point form

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

$\frac{x-3}{1}=\frac{y-5}{2}=\frac{z-3}{-2}$

let P be the coordinates of foot

$P\equiv (\lambda +3,2\lambda +5,-2\lambda +3)$

DR of $PA\equiv (\lambda +2,2\lambda +5,-2\lambda )$

So,

$(\lambda +2)1+(2\lambda +5)2+(-2\lambda )(-2)=0$

$9\lambda +12=0$

$\lambda =-\frac{4}{3}$

$P\equiv (\frac{5}{3},\frac{7}{3},\frac{17}{3})$