Q11 of 136 Page 28

Write the angle between the lines 2x = 3y = –z and 6x = –y = –4z.

We have,

2x = 3y = -z

6x = -y = -4z

The given lines can be re-written as

These lines are parallel to vectors,

and

Let θ be the angle between these lines.

Now,

cosθ

= 0

→ θ

Write the angle between the lines and

Write the direction cosines of the line whose cartesian equations are 2x = 3y = –z.

Write the value of λ for which the lines and are perpendicular to each other.

Write the formula for the shortest distance between the lines