Calculating the Dot Product: A*B

[Crauven]

I need some major help with some dot products. I was curious if when getting the dot product, you add the angles of each one to each other. I'll give the problem:

theta=(/)

Find A*B(dot product)
A=8.6i+5j
B=9.7i+2.6j

So i used the formula my teacher gave me to find the angle, theta, tan(/)=y/x. So i got the Angle for each:
tan(/)=5/8.6
(/)=tan^-1(5/8.6)
(/)=30.2

and then for B:
tan(/)=2.6/9.7
(/)=tan^-1(2.6/9.7)
(/)=15

So now, I am given two formulas to get the dot product
A*B=ABcos(/)
AB means the magnitude of A multiplied by the magnitude of B. I can get that, but it asks for one angle... what do I do? Add the two angles together? Or subtract them? I'm confused, please help!

 

[chroot]

In the formula

\vec A \cdot \vec B = || \vec A || \, || \vec B || \cos \theta

the angle \theta is the angle between the two vectors. When you found the "angle" for each vector, what you were really finding was the angle between each vector and the positive x-axis. If one vector makes an angle of 30.2 degress with the positive x-axis, and the other makes an angle of 15 degrees, the angle between them is 30.2 - 15 = 15.2 degrees.

When it doubt, draw a picture! You'll see that the two vectors make an angle of 15.2 degrees between them.

- Warren

 

[NateTG]

For the lazy among us, there's an alternative formula:
if
\vec{A}=<A_x,A_y>
and
\vec{B}=<B_x,B_y>
then
\vec{A}\cdot\vec{B}=A_xB_x+A_yB_y

 

[Crauven]

I use both formulas, the first that Warren mentioned to get the answer, then i use the lazy way to check it. Thanks guys!