Length of a vector

Find the distance between the points $P=(0,1,3)$ and $Q=(2,-1,0)$ in $\mathbb{R}^{3}$.

Find the distance between the points $P=(1,3,-1,0)$ and $Q=(2,2,3,3)$ in $\mathbb{R}^{4}$.

Describe the points in $\mathbb{R}^{3}$ that are equally distant from the two points $Q=(1,1,1)$ and $R=(-1,-1,-1)$.

Describe the points in $\mathbb{R}^{3}$ that have distance $1$ from the origin.

Find the length of each of the following vectors.

Prove that for all vectors $\mathbf{u}\in\mathbb{R}^{n}$, we have $\left\|-\mathbf{u}\right\|=\left\|\mathbf{u}\right\|$.

Which of the following are unit vectors?

Normalize the following vectors.