Show that the lines and are coplanar. Hence, find the equation of the plane containing these lines.

We know that the lines are coplanar if

Here,

x₁ = –3, x₁ = –1, y₁ = 1, y₂ = 2, z₁ = 5, z₂ = 5

l₁ = –3, l₂ = –1, m₁ = 1, m₂ = 2, n₁ = 5, n₂ = 5

= 2(–5) – 1(–10) = – 10 + 10

= 0

So the given line are coplanar .

The equation of plane contains lines is

(x + 3)(5 – 10) – (y – 1)(– 15 – (– 5)) + (z – 5)(– 6 – (– 1)) = 0

– 5x – 15 + 10y – 10 – 5z + 25 = 0

– 5x + 10y – 5z = 0

Divided by – 5

x – 2y + z = 0