Question

if v1=(2 -5) and v2=(4 -3), then the angle between the 2 vectors is______degrees. Round your answer to two decimal points

Answer 1

assuming you missed the commas; just work the definition of a dotproduct to solve for alpha:\[|\vec u||\vec v|~\cos\alpha=\vec u \cdot \vec v\]

Answer 2

not sure if definition is proper usage .. maybe identity?

Answer 3

I am still confused..

Answer 4

youll have to be more descriptive of your confusion ... my mind reading skills are subpar.

Answer 5

lol!

Answer 6

How do I find the angle based on the two points?

Answer 7

by working the setup that the dot product gives us.

Answer 8

do the dot; divide by the lengths, and inverse the cosine

Answer 9

have you learned dot product (aka inner product)?

Answer 10

I think, dont you just multiply both of the xs, and ys, and add them together

Answer 11

yes

Answer 12

yes, thats the dot process

Answer 13

lengths and inverse cosine are all thats left to determine

Answer 14

think of length is the sqrt of a vector dotted to itself ...

Answer 15

23 is the dot product!

Answer 16

(2 -5)
(4 -3)
------
8+15 = 23 correct

Answer 17

Now what do I do, you said divide by length????

Answer 18

the lengths are therefore just

(2 -5)
(2 -5)
------
4+25, sqrt(29)


(4 -3)
(4 -3)
-----
16+9, sqrt(25)

Answer 19

yes, lets work some algebra :)
\[|\vec u||\vec v|~\cos\alpha=\vec u \cdot \vec v\]
\[\cos\alpha=\frac{\vec u \cdot \vec v}{|\vec u||\vec v|}\]
\[\alpha=\cos^{-1}\left(\frac{\vec u \cdot \vec v}{|\vec u||\vec v|}\right)\]

Answer 20

\[\alpha=\cos^{-1}\left(\frac{23}{5\sqrt{29}}\right)\]

Answer 21

so the angle is the answer of that!!

Answer 22

keep in mind that the inverse is a radian measure and to convert to degrees may need a 180/pi factor

Answer 23

yes

Answer 24

so i do cos^-1(24.77)

Answer 25

depends on how accurate you need to be, but yes

Answer 26

I got domain error on my calculator

Answer 27

your division was wrong :)

23/(5sqrt(29)) is 0.85419...

Answer 28

http://www.wolframalpha.com/input/?i=arccos%2823%2F%285sqrt%2829%29%29%29

Answer 29

oh thank you so much, :))))))) You were so helpful!! the answer is 31.33!!!!

Answer 30

the domain of the inverse cosine function is -1 to 1 .... hence 24 is not in the domain

Answer 31

31.33 degrees is correct

Answer 32

good luck :)

Answer 33

Thank You!