Two non-zero vectors and are perpendicular to each other

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

Problem

Two non-zero vectors P⃗\vec P and Q⃗\vec Q are perpendicular to each other. Which one of the following quantities is necessarily zero? (a) ∣P⃗×Q⃗∣|\vec P\times\vec Q| (b) P⃗⋅P⃗\vec P\cdot\vec P (c) P⃗⋅Q⃗\vec P\cdot\vec Q (d) ∣P⃗∣ ∣Q⃗∣|\vec P|\,|\vec Q|

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