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If |A+B| = |A – B| where A and B are non zero vectors, what is the angle between them? |
|A + B| = |A - B| ==> |A + B|2 = |A - B|2 so (A+B).(A+B) = (A-B).(A-B) where "." means "scalar product". Developing the scalar products: A2 + B2 + 2A.B = u2 + v2 - 2A.B and so: A.B = 0 The angle between two vectors A and B is given by the formula
This implies cos ? = 0, the vectors are perpendicular to each other. ? = ?/2 |