Question

The co-ordinates of the foot of perpendicular drawn from point P(1, 0, 3)to the join of points A(4, 7, 1)and B(3, 5, 3)is
[RPET 2001]

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let D be the foot of perpendicular drawn fromP(1,0,3) on the line AB joining (4, 7, 1) and (3, 5, 3).
If D divides AB in ratio $\lambda :1$ then
$D=(\frac{3\lambda +4}{\lambda +1},\frac{5\lambda +7}{\lambda +1},\frac{3\lambda +1}{\lambda +1})$ .....(i)
D.r's of PD are $2\lambda +3,5\lambda +7,-2$
D.r's of AB are -1,-2,2
$\because$ $PD\perp AB;$ $\therefore -(2\lambda +3)-2(5\lambda +7)-4=0\Rightarrow \lambda =\frac{-7}{4}$
Putting the value of $\lambda$ in (i),we get the point
$D(\frac{5}{3},\frac{7}{3},\frac{17}{3})$.