Show that the lines and are coplanar. Also, find the equation of the plane containing them.

we know that line and are coplanar if

And equation of the plane containing them is

Here, equation of lines are

and

So, x₁ = – 1, y₁ = 3, z₁ = – 2, l₁ = – 3, m₁ = 2, n₁ = 1

x₂ = 0, y₂ = 7, z₂ = – 7, l₂ = 1, m₂ = – 3, n₂ = 2

so,

= 1(4 + 3) – 4(– 6 – 1) – 5(9 – 2)

= 7 + 28 – 35

= 0

So, lines are coplanar

Equation of plane containing line is

(x + 1)(4 + 3) – (y – 3)(– 6 – 1) + (z + 2)(9 – 2) = 0

7x + 7 + 7y – 21 + 7z + 14 = 0

7x + 7y + 7z = 0

X + y + z = 0