Question

(2.1) Find the components of a unit vector satisfying ~v

Answer 1

2.1) Let the vector $\vec v = \langle x, y \rangle.$

Given

$$\vec v \cdot \langle3, -1 \rangle = 0$$

Then

$$3x-y=0$$

The vector $\vec v = \langle x, 3x\rangle, x\in \R$

For example

$$x=1, \vec v=\langle1, 3\rangle.$$