Question

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

u = <6, -1>, v = <7, -4>

Answer 1

have you tried using the formula for finding the angle between two vectors?

Answer 2

solve for theta
\[\cos(\theta)=\frac{ u \cdot v}{|u||v|}\]

Answer 3

cos(theta) = 6 * 7 / |-1| |-4| ?

Answer 4

how did you get that?

Answer 5

i just plug in the numbers from the question to the formula you gave me. im sorry, i really dont know how to do this..

Answer 6

it doesn't look like you tried to find the dot product of the two vectors nor the magnitude of each vector
dot product: you multiply corresponding components and then add those results:
example:
\[<x_1,x_2> \cdot <y_1,y_2>=x_1 y_1 +x_2 y_2\]

to find the magnitude, square each component then add those results and take the square root of that sum
example:
\[|<x_1,x_2>|=\sqrt{x^2_1+x^2_2}\]

Answer 7

dot product: 42 + 4 = 46
magnitude: 36 + 1 = 37 = 6.08
?

Answer 8

\[u \cdot v=<6,-1> \cdot <7,-4>=6(7)+(-1)(-4)=42+4=46 \\ |u|=\sqrt{6^2+(-1)^2}=\sqrt{36+1}=\sqrt{37}\]
almost you forgot to take the square root

Answer 9

you still need to find |v|

Answer 10

i took the square root of 36 + 1 and got 6.08
do i find |v| then same way?

Answer 11

well if you mean by what I told you above yes
\[|<x_1,x_2>|=\sqrt{x_1^2+x^2_2}\]
this is not going to change because you have different numbers in your vector...

Answer 12

49 + 16 = 65
square root = 8.06

Answer 13

sqrt(49+16)=sqrt(65) then this will be correct

Answer 14

\[u \cdot v=46 \\ |u|=\sqrt{37} \\ |v|=\sqrt{65}\]

Answer 15

enter this into the formula I gave above and solve for theta

Answer 16

okay, so the formula is cos(theta) = u * v / |u| |v|
cos(theta) - u * v / |46| |√37|
what would be the values of u and v? <x1,y1> ?

Answer 17

you do realize the formula is:
\[\cos(\theta)=\frac{ u \cdot v}{|u||v|}\]
we already found u dot v in the numerator
and we already found ||u| and |v| in denominator

Answer 18

I even summarized these values above

Answer 19

\[u \cdot v=46 \\ |u|=\sqrt{37} \\ |v|=\sqrt{65}\]
\[\cos(\theta)=\frac{ u \cdot v}{|u||v|}\]
\[\cos(\theta)=\frac{46}{\sqrt{37} \sqrt{65}}\]

Answer 20

cos(theta) = 46 / √37 √65

Answer 21

oh, okay.. i see

Answer 22

last step solve for theta
theta is the angle after all

Answer 23

i got 60.96..

Answer 24

maybe you entered something wrong
I'm getting this:
http://www.wolframalpha.com/input/?i=arccos%2846%2F%28sqrt%2837%29*sqrt%2865%29%29%29

Answer 25

i see, so it would be 20.3 degrees

Answer 26

yes but you need to figure out what you are doing in your calculator so you can get that answer by yourself

Answer 27

yeah i know, i found out what i did wrong.

Answer 28

well that's great

Answer 29

thank you so much for your help! you are awesome!

Answer 30

it was no problem