Question: 05
Let V be an inner product space and let u and v be vectors in V. Suppose
that $||u|| = \sqrt{3}$, $||v|| = 4$ and the angle between u and v is $\frac{\pi}{6}$. Compute the
following inner products.
(a) $(u, u)$ and $(v, v)$
(b) $(u, v)$
(c) $(u + v, 2u - v)$
Question: 06
Let
$\vec{u_1} = \begin{bmatrix} 3 \ 1 \ 1 \end{bmatrix}$, $\vec{u_2} = \begin{bmatrix} -1 \ 2 \ 1 \end{bmatrix}$, $\vec{v} = \begin{bmatrix} 2 \ 3 \ -1 \end{bmatrix}$
Find (a) $Proj_{\vec{u_1}} (\vec{v})$, (b) $Proj_{\vec{u_2}} (\vec{v})$, (c) $Proj_W (\vec{v})$, where W = Span ($\vec{u_1}$, $\vec{u_2}$).
