Answer
(a) $-6.$
(b) $13.$
(c) $25.$
(d) $(-12,18).$
(e) $-30.$
Work Step by Step
Since $\mathbf{u}=(3,4), \quad \mathbf{v}=(2,-3)$, then we have
(a) $\mathbf{u} \cdot \mathbf{v}=6-12=-6.$
(b) $\mathbf{v} \cdot \mathbf{v}=4+9=13.$
(c) $\|u\|^2=\mathbf{u} \cdot \mathbf{u}=9+16=25.$
(d) $(\mathbf{u} \cdot \mathbf{v})v=-6(2,-3)=(-12,18).$
(e) $\mathbf{u} \cdot \mathbf{(5v)}=(3,4)\cdot (10,-15) =30-60=-30.$
