Question

If |a+b = la-b.
prove that the angle between a and b is 90°.​

Answer 1

Answer:

A+B|=|A-B|

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

4(A.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°) = 0.