If the straight lines and are coplanar, find the equations of the planes containing them.

We know that the lines are coplanar if

Here,

k = ±2

The equation of plane contains lines is

when k = 2

(x – 1)(4 – 4) – (y + 1)(4 – 10) + (z)(4 – 10) = 0

6y – 6z + 6 = 0

y – z + 1 = 0

The equation of plane contains lines is

When k = – 2

(x – 1)(4 – 4) – (y + 1)(– 4 – 10) + (z)(4 + 10) = 0

14y + 14z + 14 = 0

y + z + 1 = 0