Non-zero vectors satisfy and

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

Problem

Non-zero vectors p, q, r\mathbf{p},\,\mathbf{q},\,\mathbf{r} satisfy p⋅q=0\mathbf{p}\cdot\mathbf{q}=0 and q⋅r=0\mathbf{q}\cdot\mathbf{r}=0. If ∣q∣=2|\mathbf{q}|=2 and p⋅r=3\mathbf{p}\cdot\mathbf{r}=3, determine (p+q)⋅(q+r)(\mathbf{p}+\mathbf{q})\cdot(\mathbf{q}+\mathbf{r}). (a) 5 (b) 7 (c) 3 (d) 10

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