Find the angle between the line and the plane 2x + y – z = 4.

As we know that the angle θ between the line and a plane a₂x + b₂y + c₂z + d₂ = 0 is given by

……(1)

Now, given equation of the line is

So, a₁ = 1 , b₁ = – 1 and c₁ = 1

Equation of plane is 2x + y – z – 4 = 0

So, a₂ = 2, b₂ = 1, c₂ = – 1 and d₂ = – 4

∴

⇒

⇒

⇒ sinθ = 0

∴ the angle between the plane and the line is 0°