Answer
a). $-26$
b). $52$
c). $52$
d). $<78,-52>$
e). $-52$
Work Step by Step
$\mathbf{u}=<6,-4>$ and $\mathbf{v}=$
a). $\mathbf{u}\cdot\mathbf{v}=6\times(-3)+(-4)\times2=-18+-8=-26$
b). $\mathbf{u}\cdot\mathbf{u}=6\times6+-4\times-4=52$
c). $\|\mathbf{u}\|^2= \mathbf{u}\cdot\mathbf{u}=52$
d). $(\mathbf{u}\cdot\mathbf{v})\mathbf{v}=-26\mathbf{v}=<78,-52>$
e). $\mathbf{u}\cdot(2\mathbf{v})=<6,-4>\cdot=-36-16=-52$
