Question

The co-ordinates 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. $(\frac{5}{3},\frac{7}{3},\frac{17}{3})$
• B. $(5,7,17)$
• 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 A $(\frac{5}{3},\frac{7}{3},\frac{17}{3})$

$D=(\frac{3\lambda +4}{\lambda +1},\frac{5\lambda +7}{\lambda +1},\frac{3\lambda +1}{\lambda +1})\therefore \overline{AD}=(\frac{2\lambda +3}{\lambda +1},\frac{5\lambda +7}{\lambda +1},\frac{-2}{\lambda +1})$
and $\overline{BC}=(-1,-2,2)$
$\overline{AD}\perp \overline{BC}\Rightarrow -(2\lambda +3)-2(5\lambda +7)-4=0\Rightarrow \lambda =\frac{-7}{4}\therefore D=(\frac{5}{3},\frac{7}{3},\frac{17}{3})$