Find angle between vectors with cosine law

[drillman9]

Hi

I would really appreciate it if anybody could lead me in the right direction on this one...

|A| = |B|

|A+B| = 100|A-B|

I need to find the angle between A and -B for the statement to be true.

Using cosine laws I've come up with the following eqn:

|A+B| = 100|A-B|
2|A|^2 + (2|A|^2)(cosx) = 100[2|A|^2 - (2|A|^2)(cosx)]

I applied these cosine laws to the isosceles triangles

I'm not looking for the answer, I'm just looking to get some guidelines on solving for x, the angle.

Thanks so much

note: A and B are vectors.

 

[D H]

Simply divide by |A|^2 (even though A is a vector, its magnitude is a scalar) and solve for cosx.

 

[drillman9]

Ah yes, I should've know. I always over complicate myself! Thanks for the help!