Question

Find the angle between the given vectors to the nearest tenth of a degree. u = <2, -4>, v = <3, -8>

Answer 1

You can use

cos(theta) = u · v / ║u║║v║

that will come out to:

u = 2 x (-4) = -8

v = 3 x (-8) = - 24

u · v = -16

║u║ = $\sqrt{(2)^{2} + (-4)^{2} }$  = $\sqrt{20} = 2\sqrt{5}$

║v║ = $\sqrt{(3)^{2} + (-8)^{2} } = \sqrt{73}$

cos(theta)  = -16/2 $\sqrt{365}$

and to find (theta), you can now do

theta = (cos^-1) ( -16/2 $\sqrt{365}$)

I don't have a calculator, but you can solve that final problem to find theta