Question

Find the angle between the vectors u and v if u = (1, 2) and v = (- 4, - 2)

Answer 1

Use the formula \[\Large \theta = \arccos\left(\frac{u\cdot v}{|u||v|}\right)\] where u and v are vectors.

Answer 2

which number in my points do i use for each... for example which number in (1,2) would I use for which u

Answer 3

In the numerator of that fraction, you're computing the dot product between u and v

Answer 4

So what is the dot product between u = (1, 2) and v = (- 4, - 2)?

Answer 5

-8

Answer 6

good

Answer 7

now you need to find |u| and |v|

Answer 8

how do I do that?

Answer 9

use the formula

|x| = sqrt(a^2+b^2)

where the vector x is x = (a,b)

Answer 10

so it is sqrt(1^2+2^2) for u's and then sqrt(-4^2+-2^2) for v's?

Answer 11

yes, so what do you get?

Answer 12

i think u's is sqrt(5) and v's is 2sqrt(5)

Answer 13

You got it, nice work

So what is |u||v|?

Answer 14

10... so then its arccos(-8/10)?

Answer 15

yes

Answer 16

which turns out to be 143.13degrees

Answer 17

you nailed it

Answer 18

You keep helping me sooo much. Thanks, I am taking a Pre-Calculus course by myself and sometimes it can be difficult to figure out all of the questions by myself :).

Answer 19

you're very welcome, that must be pretty crazy lol

Answer 20

yep... I'm almost done though (thankfully haha)

Answer 21

well that's good

Answer 22

is there a difference between a u surrounded by two of the straight lines as opposed to the just one in the question you just helped me with?

Answer 23

Well technically it should have been \[\Large \|u\|\] since the two vertical bars denote the norm or magnitude of a vector. But the absolute value bars say the same thing (they're just used in a more general sense). So either work in my opinion.

Answer 24

oh, ok... thanks for clarifying. I am working on another type of question like that and wasn's sure if there was a difference.

Answer 25

there's not much of a difference really