What is the Angle Between Two Vectors with Equal Magnitudes and a Given Sum?

[Melchior25]

Hey everyone,

So I'm completely stumped on this question and I have no clue on how to even start. Any help would be greatly appreciated.

Vectors A and B have equal magnitudes of 23.0. If the sum of A and B is the vector 12.1 j, determine the angle between A and B.

Thanks in advance.

 

[rock.freak667]

Draw the resultant vector of magnitude 12.1N first, then draw the two vectors A and B that would give the resultant direction in the direction that you drew the 12.1N force in. Complete the parallelogram. Then use some trigonometry.

 

[Shooting Star]

In this case, to save a lot of time, I would suggest the OP just use the formula for the magnitude of the resultant R of two forces P and Q, given by:

R^2 = P^2 + Q^2 + 2PQcos(theta).

The magnitude of R is given.

 

[Feldoh]

Yeah I could agree, just use the law of cosines.