Question

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

Answer 1

this assumes you know the dot product equivalence

Answer 2

\[|u||v|~\cos(\alpha)=u\cdot v\]

Answer 3

otherwise you use the law of cosine

Answer 4

@amistre64 the law of cosines is a^2=b^2+c^2-2bc*cos(A) right?

Answer 5

yes, so we still have to determine the length of the other side

Answer 6

how do I know what is a and b

Answer 7

b and c are the lengths of the vectors stated, since a is across from A

Answer 8

a is the length of the vector defined as v1-v2

Answer 9

(-6, 8)

Answer 10

v1=(-2, 5)
-v2=(-4, 3)

-6,8 is fine for vector a

how do we determine lengths?

Answer 11

is that Pythagorean Theorem a^2 +b^2 =c^2

Answer 12

yep

square, add, sqrt the parts .... pythagorean style

sqrt(4+25)
sqrt(16+9)
sqrt(36+64)

Answer 13

i spose the sqrting is not required at the moment

Answer 14

29
25
100

Answer 15

100 = 25 + 29 - 2(sqrt(25))(sqrt(29)) cosA

yep

Answer 16

what do I plug in for A

Answer 17

A is the angle you are looking for

Answer 18

so do i solve this 25 + 29 - 2(sqrt(25))(sqrt(29)) cosA

Answer 19

yeah, thats what the parts filled in look like

equate it to 100 of course

Answer 20

a^2 = b^2 + c^2 -2cb cosA


b^2 + c^2 - a^2
-------------- = cosA
2cb

Answer 21

is a=29 b=25 and c=100? is so I got 1223/625 =1.9568 or 1.96

Answer 22

a^2=100
b^2=25
c^2=29

Answer 23

54-100
----------
2(5)sqrt(29)


5.4-10
----------
sqrt(29)


-4.6
----------
sqrt(29)

cos^(-1)(-46/sqrt(29))

Answer 24

-0.8541
-0.8541
-0.8541

Answer 25

-8.54068457

or -8.54

Answer 26

i forgot how to add .... regardless

http://www.wolframalpha.com/input/?i=cos%5E%28-1%29%28%2825%2B29-100%29%2F%282*sqrt%2825%29*sqrt%2829%29%29

Answer 27

2.59?

Answer 28

do they want radians or degrees?

Answer 29

when I add those three up i get -2.5623

Answer 30

it did not specify all it says is to round your answer to two decimal places

Answer 31

25+29-100 = -46

-46/2(5)(sqrt(29)) = -23/5sqrt(29)

Answer 32

then its either 2.59 radians

or 148.67 degrees

Answer 33

im thinking its degrees they want but its just a hunch

Answer 34

oh ok yeah I guess if they say angle 148.67 degrees might be it then

Answer 35

im sorry I looked at the picture they want degrees

Answer 36

thank you :)

Answer 37

youre welcome