Consider the three vectors in $\mathbb{R}^2 . \mathbf{u}=\langle 1,1), \mathbf{v}=\langle 4,2), \mathbf{w}=(1,-3)$. For each of the following vector calculations:
- [P] Perform the vector calculation graphically ${ }^t$, and draw the resulting vector.
- Calculate the vector calculation arithmetically and confirm that it matches your picture.
(a) $3 \mathbf{u}+2 w$
(b) $\mathbf{u}+\frac{1}{2} \mathbf{v}+\mathbf{w}$
(c) $2 \mathrm{v}-\mathrm{w}-7 \mathrm{u}$