Question

Help? (:
Find the angle between the given vectors to the nearest tenth of a degree.

u = <6, -1>, v = <7, -4>

Answer 1

I got .94.. But that's not even close to one of my choices..

Answer 2

@mathmale You busy? :p

Answer 3

i will help

Answer 4

u•v = ||u|| ||v|| cosθ

u•v = <6,-5> • <-5,-3> =
(6)(-5) + (-5)(-3) = -15

||u|| = √((6)²+(-5)²) = √(61)
||v|| = √((-5)²+(-3)²) = √(34)

u•v = ||u|| ||v|| cosθ
-15 = √(61) √(34)cosθ
-15 = √(2074)cosθ
cosθ = -15√(2074)

θ = arccos(-15/√(2074))

θ = 109.2°

Answer 5

got it

Answer 6

can you draw this batman?

Answer 7

u•v = ||u|| ||v|| cosθ is one of the definitions of the dot product of two vectors, BatGirl.
As Kat has demonstrated, this equation can be solved for cos theta, where theta is the angle between the two vectors.

Once you have that (cos theta), you can use the inverse cosine function to find the angle itself. Be sure to specify whether you have this angle in radians or degrees.

Answer 8

So I just do the same thing, but with my numbers?

Answer 9

I got the same thing.. What the poop?

Answer 10

@katragaddasaichandra

And no @jeremyggg

Answer 11

I'm probably just making a dumb math error.

Answer 12

Break the problem down into steps. You'll need to find the dot product: u dot v. Then you'll need to find the magnitudes of both u and v, multiply these magnitudes together, and then divide that product into u dot v.

Care to try this, showing your work?

Answer 13

I got 46 for u dot v.

Answer 14

Then the bottom.. sqrt(37) dot sqrt(65), 49.04.

Answer 15

Then wouldn't I divide 46 by 49.04...?

Answer 16

Am I doing something wrong @mathmale ?

Answer 17

Hello? :C

Answer 18

Give me a minute or two and I'll go thru the problem quickly myself, so we have something to compare.

Answer 19

sqrt(37) dot sqrt(65), 49.04: Not dot product here; just simple multiplication. But your result is correct: 49.041.
Also, y our dot product from earlier, 46, is correct.

Let's divide 49.041 into 46. This is exactly what y ou proposed to do earlier.

Answer 20

Have you performed this division yet? If not, please do it.

Answer 21

46/49.041 = ?

Answer 22

Sorry... .9379=.94

Answer 23

As Kat has demonstrated, this equation can be solved for cos theta, where theta is the angle between the two vectors.

Once you have that (cos theta), you can use the inverse cosine function to find the angle itself. Be sure to specify whether you have this angle in radians or degrees.

Your 0.9379 is the cosine of theta. We are to find theta itself.

First, set your calculator to RADIAN mode, and then type in \[\cos ^{-1} 0.938\]

Answer 24

.354?

Answer 25

Yes, that's your angle, theta, in radians. You could easily show that this angle is approx. 20.28 degrees.

Answer 26

How do I find the degree?

Answer 27

Use the conversion factor Pi=180 deg.:\[(0.354 rad)(\frac{ 180 }{ \pi rad }=?\]

Answer 28

or simply re-set your calculator, this time to DEGREE mode, and find arccos 0.938 again. U should get the same result.

Great working with you! I'd like to get off the computer now, however.

Answer 29

Oh, I got it! Thank you so much! God bless you! <3

Answer 30

saimouli!!

Answer 31

Do what?