How Do You Calculate the Angle Between Two Vectors?

[azila]

Easy problem that I am stuck on...

Homework Statement

Two vectors A and B have magnitude of A = 3.02 B=3.00. Their vector product is AXB = -4.90k + 2.01i. What is the angle between vector A and vector B?

Homework Equations

since I know the vector product of A and B, I was thinking that Cx = 2.01 and Cz = -4.90. I would then add them together to get -2.89. Then could i use the equation C = ABsin(theta). That would be like

-2.89 = (3.02)(3.00)sin(theta)
-.319=sin(theta)
-18.6 = theta
I don't know if this is the right path to follow but this is what I could come up with.

The Attempt at a Solution

THANKS for any help.

 

[rootX]

it's
$$\left| c\right| =\left| a\right| \,\left| b\right| \,sin\left( p\right)$$
where c = a x b

 

[azila]

so am I solving it incorrectly because i am using the same equation, its just that I don't know if the value of c that I have is correct. Also the answer I get is not right. So, what should I change? thanks for the help though.

 

[rootX]

get the absolute value of c.
c^2=x^2+y^2+z^2

 

[azila]

Thank You So Much! I Realized What I Was Doing Wrong Was That I Was Taking The Sin When I Should Have Been Taking The Arcsin. Thanks Again!