Question

The perpendicular distance of a corner of a unit cube from a diagonal not passing through it is

• A. $\sqrt{\frac{1}{3}}$
  
• B. $\sqrt{\frac{2}{3}}$
  
• C. 1
• D. none of these

Answer 1

The correct option is B $\sqrt{\frac{2}{3}}$


Let OA, OB, OC be the edges of unit cube

Hence, $\underset{OA}{\to }=\hat{i},\underset{OB}{\to }=\overrightarrow{j},\underset{OC}{\to }=\overrightarrow{k},$
If CM is the perpendicular from C to the diagonal OP
Them $OM=\underset{OC}{\to }.\widehat{OP}$
$=\hat{k}.\frac{(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}}=\frac{1}{\sqrt{3}}O{C}^2=O{M}^2+C{M}^2\therefore CM=\sqrt{\frac{2}{3}}$