For any non-zero vectors and

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

For any non-zero vectors a\mathbf{a} and b\mathbf{b}, let θ\theta be the angle between them. Which one of the following equals cos⁡θ\cos\theta? (a) a⋅b∣a∣2+∣b∣2\dfrac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}|^{2}+|\mathbf{b}|^{2}} (b) a⋅b∣a∣ ∣b∣\dfrac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}|\,|\mathbf{b}|} (c) ∣a∣ ∣b∣a⋅b\dfrac{|\mathbf{a}|\,|\mathbf{b}|}{\mathbf{a}\cdot\mathbf{b}} (d) (a⋅b)2(∣a∣ ∣b∣)2\dfrac{(\mathbf{a}\cdot\mathbf{b})^{2}}{(|\mathbf{a}|\,|\mathbf{b}|)^{2}}

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