Question

The distance of the point P(-2, 3, 1) from the line QR which passes through the point Q(-3, 6, 2) and makes equal angles with the axes is

• A. $3$
• B. $8$
• C. $\sqrt{2}$
• D. $2\sqrt{2}$

Answer 1

The correct option is D $2\sqrt{2}$

According to question $co{s}^2\alpha +co{s}^2\alpha +co{s}^2\alpha =1$
$\therefore cos\alpha =\frac{1}{\sqrt{3}}$
$\therefore$ DC's are $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{3}PQ=\sqrt{1+9+1}=\sqrt{11}$
QM = Projection of PQ on QR
$=|(-2+3)\frac{1}{\sqrt{3}}+(3-6)\frac{1}{\sqrt{3}}+(1-2)\frac{1}{\sqrt{3}}|$
$=|\frac{1}{\sqrt{3}}-\frac{3}{\sqrt{3}}-\frac{1}{\sqrt{3}}|=\sqrt{3}\therefore PM=\sqrt{(QP{)}^2-(QM{)}^2}$
$=\sqrt{11-3}=2\sqrt{2}$