Define the inner product in the usual manner
$<\vec{x}, \vec{y}> = x_1y_1 + x_2y_2 + ... + x_ny_n$
for vectors in
$\mathbb{R}^n$
Also define the norm $||\vec{x}|| = \sqrt{<\vec{x}, \vec{x}>}$.
Find $<\vec{v}, \vec{w}>$ and $||\vec{v}||$.
Where we have $\vec{v}, \vec{w}$ defined as:
$\vec{v} = \begin{bmatrix} 4\\1\\-2\\1 \end{bmatrix}$ and $\vec{w} = \begin{bmatrix} 3\\-4\\2\\-4 \end{bmatrix}$.
