Show that the lines and intersect.

Also, find their point of intersection.

Given equations :

To Find : d

Formula :

1. Cross Product :

If are two vectors

then,

2. Dot Product :

If are two vectors

then,

3. Shortest distance between two lines :

The shortest distance between the skew lines and

is given by,

Answer :

For given lines,

Here,

Therefore,

Now,

= 0 + 12 – 6

= 6

Therefore, the shortest distance between the given lines is

As d ≠ 0

Hence, the given lines do not intersect.