Answer
(a) $\mathbf{u} \cdot \mathbf{v}=-6.$
(b) $\mathbf{v} \cdot \mathbf{v}=8.$
(c) $\|u\|^2=\mathbf{u} \cdot \mathbf{u}= 5.$
(d) $(\mathbf{u} \cdot \mathbf{v})v=(-12,12).$
(e) $\mathbf{u} \cdot \mathbf{(5v)}=-30.$
Work Step by Step
Since $\mathbf{u}=(-1,2), \quad \mathbf{v}=(2,-2)$, we have
(a) $\mathbf{u} \cdot \mathbf{v}=-2-4=-6.$
(b) $\mathbf{v} \cdot \mathbf{v}=4+4=8.$
(c) $\|u\|^2=\mathbf{u} \cdot \mathbf{u}=1+4= 5.$
(d) $(\mathbf{u} \cdot \mathbf{v})v=-6(2,-2)=(-12,12).$
(e) $\mathbf{u} \cdot \mathbf{(5v)}=(-1,2)\cdot (10,-10) =-10-20=-30.$
