A ray of light, travelling in the direction 1 2 i ^ + 3 j ^ , is incident on a plane mirror. After reflection, it travels along the direction 1 2 i ^ - 3 j ^ . The angle of incidence is

Step-by-step solution

α = angle between vectors cos α = 1 2 i ^ + 3 j ^ · 1 2 i ^ - 3 j ^ i ^ + 3 j ^ i ^ - 3 j ^ = 1 4 1 - 3 1 × 1 = - 2 4 = - 1 2 α = 1 2 0 ° = 2 π 3 ∴ π - α = 2 θ π = 2 π 3 = 2 θ θ = π 3 × 2 = π 6 = 3 0 °