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) }` =
`√(20) = 2√(5)`

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

cos(theta) = -16/2
`√(365)`

and to find (theta), you can now do

theta = (cos^-1) ( -16/2
`√(365)`)

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