Question

two forces have the same magnitude F, what is the angle between the two vectors if their sum has a magnitude of (a) 2F? (b) sqrt of 2F (c) zero? Sketch the three vectors in each case.

Answer 1

in case a, line both up head-to-tail in a straight line... that's the only way to get a sum 2F
in case b, sqrt(2) is the length of the hypotenuse in a 45 degree triangle, so the vectors must be at 90 degrees to each other
in c) lined up head to tail, the only way to get 0 is if they point in opposite direction

Answer 2

oh.. so is it right to answer arc tan (F/F)? :|

Answer 3

I don't think so - arctan(1) is always the same, but the answers above are not the same