Question

The shortest distance between a diagonal of a cube of edge-length one unit and the edge not meeting it, is –

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

Answer 1

Answer: (B)

$\frac { 1 } { \sqrt { 2 } }$

Answer 2

dr’s of diagonal through the origin are (1, 1, 1)

dr's of edge, parallel to x-axis

and in the plane z = 0, are (1, 0, 0)

Hence d.c. of the line of shortest distance are $\left( 0 , \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } \right)$

Projection of line segment joining (1, 1, 1) and (1, 1, 0) on the line of shortest distance = – $\frac { 1 } { \sqrt { 2 } }$