Question

Pls help with this pre-calc problem

Answer 1

we are given

$v_1=(2,-6)$

$v_2=(-4,7)$

(a)

we can find absolute value

$|v_1|=\sqrt{(2)^2+(-6)^2}$

$|v_1|=2\sqrt{10}$

$|v_2|=\sqrt{(-4)^2+(7)^2}$

$|v_2|=\sqrt{65}$

(b)

we can find unit vectors

$v_1'=\frac{v_1}{|v_1|}$

now, we can plug values

$v_1'=\frac{(2,-6)}{2\sqrt{10}}$

$v_1'=(\frac{1}{\sqrt{10}} ,\frac{-3}{\sqrt{10}} )$

$v_2'=\frac{v_2}{|v_2|}$

now, we can plug values

$v_2'=\frac{(-4,7)}{\sqrt{65}}$

$v_2'=(\frac{-4}{\sqrt{65}} ,\frac{7}{\sqrt{65}} )$

(c)

we can draw vectors