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°