Question

Let the unit vectors a and b  be perpendicular and the unit vector c be inclined at an angle θ to both vector a and vector b. If vector c = αa + βb + γ(a x b), then

(A) α = β = cosθ, γ² = cos2θ

(B) α = β = cosθ, γ² = - cos2θ

(A) α = cosθ, β = sinθ, γ² = cos2θ

(D) None of these

Answer 1

Answer is (B) α = β = cosθ, γ² = - cos2θ

We have,

Taking dot product by vector a, we get

Taking dot product of Eq. (1) by vector b, we get

α = β = cosθ, γ² = - cos2θ