Question

Find the shortest distance between the given lines.

vectors r = (i + j) + λ(2i - j + k),

r = (2i + j - k) + μ(3i - 5j + 2k).

Answer 1

Given equations :

To Find : d

Formula :

1. Cross Product :

If a & b are two vectors

3. Shortest distance between two lines :

The shortest distance between the skew lines \(\vec r=\bar a_1+\lambda \bar{b_1}\) and

\(\vec r=\bar a_2+\lambda \bar {b_2}\) is given by,

For given lines,

= 3 + 0 + 7

= 10

Therefore, the shortest distance between the given lines is