Question

If |A+B|=|A|+|B| then the angle between the vectors A and B is *0 *180 *90 ?

Answer 1

`abs( mathbf A + mathbf B)^2 = ( mathbf A + mathbf B) cdot ( mathbf A + mathbf B)`

`= | mathbf A |^2 + | mathbf B|^2 + mathbf A cdot mathbf B + mathbf B cdot mathbf A`

As scalar product commutes:

`implies abs( mathbf A + mathbf B)^2 = | mathbf A |^2 + | mathbf B|^2 + 2 |mathbf A| | mathbf B | cos alpha qquad square`

If `|mathbfA+mathbfB|=|mathbfA|+|mathbfB|`

Then also by squaring each side:

`|mathbfA+mathbfB|^2=|mathbfA|^2+|mathbfB|^2 + 2 |mathbfA||mathbfB| qquad triangle`

`square = triangle implies cos alpha = 1, alpha = 0`