Question

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

u = <2, -4>, v = <3, -8>

Answer 1

Dot product!

\[ \vec u \cdot \vec v = | \vec u ||\vec v | \cos \theta\]

Answer 2

so we know that
u dot v / |u||v| = cos(t)

Answer 3

what?

Answer 4

Sorry, I take this class online, it's really hard for me to understand what im doing...

Answer 5

No worries :) The dot product is an operation that multiplies the x terms and the y terms (and z, etc...) of two vectors and adds them together.

\[ \vec u \cdot \vec v = (2)(3) + (-4)(-8)\]

Answer 6

It's also called the "scalar product" because it takes two vectors and generates a scalar number from their components.

Answer 7

The dot product is also a measure of the angle between two vectors, so, like before

\[ \vec u \cdot \vec v = |\vec u||\vec v| cos \theta \]

Answer 8

so 6 + 32 = 38?

Answer 9

is that what that means?

Answer 10

Yeah. That's the left hand side. For the right hand side you take the magnitude of the two vectors and multiply them together.

\[ |\vec u| = \sqrt{2^2 + (-4)^2} \\ |\vec v| = \sqrt{3^2 + (-8)^2}\]

Then that goes in front of the cos

Answer 11

Okayyyyy...

Answer 12

Have you not seen any of the before ?

Answer 13

Yea, I have, it's just always been confusing for me because of me not having a teacher to explain it to me. Literally all I have in the way of help is a bunch of words, like a text book but not as good...

Answer 14

As long as it's not all a bunch of new gibberish :) And it's confusing no matter what, so don't feel bad. What about the stuff above makes sense? Or at least is less confusing?

Answer 15

It's less confusing yea, so thanks! I can probably figure out the rest now, I hope lol

Answer 16

Well I can help if you need clarification. Just holler :)