Question

Find the angle between the given vectors to the nearest tenth of a degree.

u = <-5, -4>, v = <-4, -3>

Answer 1

Hi! I can help you! :)

Answer 2

Do you have any ideas about how to get started, or are you completely stuck? :)

Answer 3

Hint...dot product

\[\large \vec{u} \cdot \vec{v} = ||u|||v|| \cos(\theta)\]

So

\[\large cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{||u|| ||v||}\]

Answer 4

@BasketWeave completely stuck :-(

Answer 5

Okay, no problem! John's given you a clue here: we can use the dot product.

Answer 6

Do you know how to find the dot product between two vectors? :)

Answer 7

u * v = <-5,-4> , <-4,-3> =-5(-4) + -4(-3) = 20 + 12 = 32

|u| = √(-5)^2 + (-4)^2 =√25 +16 = √41

Answer 8

|v| = √(-4)^2 + (-3)^2 = √16 + 9 = √25 = 5

Answer 9

u * v = 32
|u| =√41
|v| = 5

Answer 10

\[\frac{ 32 }{ \sqrt{41}5} \]

Answer 11

Well done :) Carry on...

Answer 12

im getting 0.02648....

Answer 13

i calculated wrong

Answer 14

now i got, 0.99951..

one of my answer choices is 0.9 degrees, is that correct?

Answer 15

Well, try and remember what that 0.99951 means... :) It's not actually the angle!

Answer 16

Right, that leaves us with

\[\large cos(\theta) = 0.99951\]

What do you get when you actually solve for the angle?

Answer 17

1.8 degrees?

Answer 18

Excellent, well done!

Answer 19

Correct indeed

Answer 20

thank you guys so much for your help!

Answer 21

You're most welcome :)