Let the unit vectors {a} and {b} be perpendicular to each other and the unit vector {c} be inclined at an angle \\theta to both a and {b}. If {c}=\\alpha{a}+\\beta{b}+\\gamma({a} \.{b}), where \\alpha, \\beta, \\gamma are scalars, then

Correct Answer is : α=cosθ,β=cosθ,γ2=cos2θ

\\alpha=\cot \\theta, \\beta=\sin \\theta, \\gamma^{2}=\cos 2 \\theta

\\alpha=\cos \\theta, \\beta=\cos\\theta, \\gamma^{2}=\cos 2 \\theta

\\alpha=\cos \\theta, \\beta=\sin\\theta, \\gamma^{2}=\cos 2 \\theta

\\alpha=\sin\\theta, \\beta=\cos\\theta, \\gamma^{2}=-\cos 2 \\theta

AMU Engineering 2019 solved paper Solved Paper

Section: Mathematics

Question : 147 of 150

Marks: +1, -0

Let the unit vectors a and b be perpendicular to each other and the unit vector c be inclined at an angle θ to both a and b. If c=αa+βb+γ(a.b), where α,β,γ are scalars, then

α=cot‌θ,β=sin‌θ,γ2=cos‌2‌θ
α=cos‌θ,β=cos‌θ,γ2=cos‌2‌θ
α=cos‌θ,β=sin‌θ,γ2=cos‌2‌θ
α=sin‌θ,β=cos‌θ,γ2=−cos‌2‌θ

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