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

……(1)

Given that the line is passing through A(3, – 4, – 2) and (12, 2, 0)

∴ the direction ratios of line AB are

= (12 – 3, 2 – (– 4), 0 – (– 2))

= (12 – 3, 2 + 4, 0 + 2)

= (9, 6, 2)

So,

a₁ = 9, b₁ = 6 and c₁ = 2 ……(2)

Given equation of plane is 3x – y + z = 1

So,

a₂ = 3, b₂ = – 1 and c₂ = 1 ……(3)

∴

⇒

⇒

⇒ θ = sin ^{– 1} ()

Therefore the required angle is sin ^{– 1} ()