Question

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

Answer 1

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

$$3v_1-v_2=0=>v_2=3v_1$$

$$|\vec v|=1=>v_1^2+v_2^2=1$$

$$v_1^2+(3v_1)^2=1$$

$$v_1=\pm\dfrac{\sqrt{10}}{10}$$

$$\vec v=\langle-\dfrac{\sqrt{10}}{10}, -\dfrac{3\sqrt{10}}{10}\rangle$$

or

$$\vec v=\langle\dfrac{\sqrt{10}}{10}, \dfrac{3\sqrt{10}}{10}\rangle$$