Ask a Teacher

if |A+B|=|A-B|,A&B are non zero vectors,what is the angle btw 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