Mathematics

Problem

Non-zero vectors

\mathbf{p},\,\mathbf{q},\,\mathbf{r}

satisfy

\mathbf{p}\cdot\mathbf{q}=0

and

\mathbf{q}\cdot\mathbf{r}=0

. If

|\mathbf{q}|=2

and

\mathbf{p}\cdot\mathbf{r}=3

, determine

(\mathbf{p}+\mathbf{q})\cdot(\mathbf{q}+\mathbf{r})

. a) 5 b) 7 c) 3 d) 10