we are given
[tex] v_1=(2,-6) [/tex]
[tex] v_2=(-4,7) [/tex]
(a)
we can find absolute value
[tex] |v_1|=\sqrt{(2)^2+(-6)^2} [/tex]
[tex] |v_1|=2\sqrt{10} [/tex]
[tex] |v_2|=\sqrt{(-4)^2+(7)^2} [/tex]
[tex] |v_2|=\sqrt{65} [/tex]
(b)
we can find unit vectors
[tex] v_1'=\frac{v_1}{|v_1|} [/tex]
now, we can plug values
[tex] v_1'=\frac{(2,-6)}{2\sqrt{10}} [/tex]
[tex] v_1'=(\frac{1}{\sqrt{10}} ,\frac{-3}{\sqrt{10}} ) [/tex]
[tex] v_2'=\frac{v_2}{|v_2|} [/tex]
now, we can plug values
[tex] v_2'=\frac{(-4,7)}{\sqrt{65}} [/tex]
[tex] v_2'=(\frac{-4}{\sqrt{65}} ,\frac{7}{\sqrt{65}} ) [/tex]
(c)
we can draw vectors
