Question

For what angle between A and B, |A+B|=|A-B|​

Answer 1

Answer:

90

Explanation:

I assume the question means |A+B|=|A-B| where A and B are non-zero vectors.

Squaring both sides,

|A+B|2=|A−B|2

Since A.A=|A|2

|A+B|2=|A−B|2

(A+B).(A+B)=(A−B).(A−B)  

A.A+A.B+B.A+B.B=A.A−A.B−B.A+B.B ( Using distributive property)

|A|2+2A.B+|B|2=|A|2−2A.B+|B|2

4A.B=0

A.B=0

|A||B|cos(theta)=0

Since A and B are non-zero vectors, A and B must be perpendicular as cos (90 degrees) = 0