Question

The line through the point $P$ parallel to line $L$ meet the plane at $Q$ & foot of the perpendicular drawn from the point $P$ meet the plane $\pi$ at $M$, then $QM$ equals

• A. $5\sqrt{78}$ units
• B. $3\sqrt{78}$
• C. $\sqrt{78}$
• D. $\frac{5}{3}\sqrt{78}$

Answer 1

The correct option is D $\frac{5}{3}\sqrt{78}$

From solution of question (1) & question (3), we have
$Q=(6,-8,13)$ and $M(\frac{8}{3},\frac{11}{3}.\frac{14}{3})$
$\therefore$ $QM=\sqrt{(6-\frac{8}{3})+{(-8-\frac{11}{3})}^2+{(13-\frac{14}{3})}^2}$

$=\sqrt{{\left(\frac{10}{3}\right)}^2+{\left(\frac{-35}{3}\right)}^2+{\left(\frac{25}{3}\right)}^2}$

$=\frac{1}{3}\sqrt{100+1225+625}$

$=\frac{1}{3}\sqrt{1950}$

$=\frac{5}{3}\sqrt{78}$