Question

If v1=(2,-5) and v2=(4,-3), then the angle between the vectors is _____. Round your answer to two decimal places.

Answer 1

\[v_1\cdot v_2=|v_1|~|v_2|~\cos\theta\]

Answer 2

Do I add any of terms together or something?

Answer 3

You could say that. Do you know how to find the dot product of two vectors?

Answer 4

Like 2 + 4? and -5 + -3?

Answer 5

Not quite, no.

Given \(a=\langle a_1,a_2\rangle\) and \(b=\langle b_1,b_2\rangle\), then the dot product of \(a\) and \(b\) is \(a\cdot b=a_1b_1+a_2b_2\)

Answer 6

so the answer is 23?

Answer 7

Yep

Answer 8

Now just get ||u|| and ||v||

Answer 9

uh how do I do that?

Answer 10

It's pythagorean theorem actually.
\[||u||=\sqrt{(a)^{2}+(b)^{2}}\] whichever letters you like. It's just like a^2 + b^2 = c^2. So for u, calculate:
\[||u||= \sqrt{(2)^{2}+(-5)^{2}}\]

Answer 11

i got 5.38

Answer 12

and for v i got 5

Answer 13

So multiply those two results and then divide that into 23 and that'll = cos(theta)

Answer 14

is it .39?

Answer 15

wait was I suppose to take the answer from dividing it by 23 and put that answer into cos(theta)? @Psymon

Answer 16

\[\frac{ 23 }{ (5)(5.38) }=\cos \theta \]

Answer 17

24.75

Answer 18

For theta?

Answer 19

I got 31.24.

Answer 20

for 23/(5)95.38)

Answer 21

23 is divided by the product of those 2.

Answer 22

Oh so 31.24 would be my final answer?

Answer 23

And again, I think it's a good habit to keep it in radical form as long as possible xD And yes, it would.

Answer 24

thanks!

Answer 25

Yep yep.