Exercise 3. (3pts+4pts+2pts)
Let u = (1,2,3,1,1), v = (0,1,-2,3,0), w = (1,-1,1,1,0).
Compute the following.
a. The distance between u and v.
b. The angle (in radian) between u and w.
c. The unit vector in the direction of v.
Exercise 4. (10 pts)
Let $u = \begin{bmatrix} 2 \ -1 \ -1 \ \end{bmatrix}$, $v = \begin{bmatrix} -2 \ -5 \ 1 \ \end{bmatrix}$, and $w = \begin{bmatrix} 1 \ 2 \ 3 \ \end{bmatrix}$. Use the Orthogonal Decomposition Theorem to
write w as $\omega + z$ where $\omega \in W = \text{span}\{u, v\}$ and $z \in W^\perp$.
