Question

Show that the lines vectors r = (2i - 3k) + λ(i + 2j + 3k) and r = (2i + 6j + 3k) + μ(2i + 3j + 4k) intersect. Also, find their point of intersection.

Answer 1

Given equations :

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 x 0) + (2 x 6) + ((-1) x 6)

= 0 + 12 – 6

= 6

Therefore, the shortest distance between the given lines is

As d ≠ 0

Hence, the given lines do not intersect.