Question

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

u = <8, 7>, v = <9, 7>

@agent0smith

Answer 1

\[|u|~|v|~cos~\alpha=u\cdot v\]
solve for alpha

Answer 2

a · b = |a| × |b| × cos(θ)

Find a*b first, like in the last question.

Answer 3

so 8*9 and 7*7?

Answer 4

yes, and add the results

Answer 5

8*9 + 7*7 = |a| × |b| × cos(θ)

find |a| and |b|, just use pythagoras to find their magnitudes

Answer 6

72+49=121

Answer 7

so from there what would i do>

Answer 8

find |a| and |b|, just use pythagoras to find their magnitudes

Answer 9

121 = |a| × |b| × cos(θ)

All you need to do is find the magnitude of a and b, then find cosθ

Answer 10

For a vector w = <a, b>
\[\Large |w| = \sqrt{a^2+b^2}\]ie use pythag basically.

Answer 11

i got like 87

Answer 12

For what?

Answer 13

u = <8, 7>

Find |u|


v = <9, 7>

Find |v|

Answer 14

i feel so dumb

Answer 15

haha why?

Answer 16

i am so lost

Answer 17

If you had w = <4, 2> and need |w|
\[\Large |w| = \sqrt{4^2+2^2} = \sqrt{20}\]

Answer 18

Find |u| and |v| in the same way.

Answer 19

u= \[\sqrt{113}\]
v=\[\sqrt{130}\]

Answer 20

Good, so \[\Large 121 = \sqrt{113} \sqrt{130} × \cos(θ)\]now find cos(θ)

Answer 21

how lol

Answer 22

Could you do it if it was this?\[\Large 4 = 2 \times 3 \times \cos \theta\] If so, do the same thing!

Answer 23

Just get cosθ by itself.

Answer 24

so would it be 3.4 or something close to that

Answer 25

No, show me or tell me what you did.

Answer 26

i did sqrt of 113 timess sqrt of 130 then the answer i got i divided by 121

Answer 27

If you had 4=2×3×cosθ you would divide both sides by 6 right?

Answer 28

yes

Answer 29

So with \[\Large 121 = \sqrt{113} \sqrt{130} × \cos(θ)\]do the same thing... you might notice the mistake you made.

Answer 30

okay so when i i multiply the squre roots together i get 35.9, then i divided that by 121 and got 3.3 do i have to find the cos of that

Answer 31

If you had \[\Large 2 = 5 x\]you would divide both sides by 5 right? To get \[\Large \frac{ 2 }{ 5} = x\]
You're doing things in the wrong order.

Answer 32

You're doing something weird with the square roots, actually... 35.9?? http://www.wolframalpha.com/input/?i=sqrt113+*+sqrt130

Answer 33

121=121.2*cos(θ)

Answer 34

Yes, now find the angle theta.

Answer 35

would i divide it now?

Answer 36

Yes, then find theta.

Answer 37

i got when i divided 0.9983498

Answer 38

0.9983498 = cosθ

Find θ

Answer 39

Use a calculator and the inverse cosine button

Answer 40

Inverse cosine right!

Answer 41

holy poop please tell me is that haha i've been here trying to figure it out

Answer 42

i got 3.292
so rounded 3.3

Answer 43

Looks about right

Answer 44

YAY finally lololol THANK YOU SO MUCH!! you are amazing

Answer 45

Haha you're welcome :)