We know that line is parallel to plane a₂x + b₂y + c₂z + d₂ = 0 if a₁a₂ + b₁b₂ + c₁c₂ = 0 is given by

……(1)

Now, given equation of line is

So, a1 = 3 , b1 = – 1 and c1 = 2

Equation of plane is 3x + 4y + z + 5 = 0

So, a2 = 3, b2 = 4, c2 = 1 and d2 = – 5

∴

⇒

⇒

⇒ sinθ = ⇒ θ = sin ^{– 1}(

∴ the angle between the plane and the line is sin ^{– 1}(