The shortest distance between the lines and is

We have,

→ (1)

→ (2)

We know that line (1) passes through the point (3, 8, 3) and has direction ratios proportional to 3, -1, 1.

It’s vector equation is –

, where and

Also, line (2) passes through the point (-3, -7, 6) and has direction ratios proportional to -3, 2, 4.

It’s vector equation is –

, where and

Now,

= 36 + 225 + 9

= 270

The shortest distance between the lines, and is given by,

d