Two unit vectors and satisfy

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

Problem

Two unit vectors p⃗\vec{p} and q⃗\vec{q} satisfy p⃗ ⋅ q⃗<0\vec{p}\,\cdot\,\vec{q}<0. Which statement about the angles θp\theta_p and θq\theta_q they make with the positive xx–axis is necessarily true? (a) ∣θp+θq∣=180∘|\theta_p+\theta_q|=180^{\circ} (b) ∣θp−θq∣<90∘|\theta_p-\theta_q|<90^{\circ} (c) ∣θp−θq∣>90∘|\theta_p-\theta_q|>90^{\circ} (d) ∣θp−θq∣=90∘|\theta_p-\theta_q|=90^{\circ}

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