How Is the Angle Between Two Vectors Determined Using Their Dot Product?

[StephenDoty]

One vector has a length of 23 units and another a length of 12 units. If the scalar product of these two vectors is 113, what is the angle between the two vectors?

A dot B = ABcos(theta)
113 = 12*23*cos(theta)
113/276= cos(theta)
cos^(-1)113/276 = theta
65.8 degrees or 66 degrees using sig figs = theta

is this right?

 

[neu]

yes yes

 

[physixguru]

easy.