Question

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

Answer 1

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Answer 2

Hii dear,

# Given-
|A+B| = |A-B|

# To prove-
θ = 90°

# Proof-
Let θ be the angle between A and B.
|A+B|^2 = |A|^2 + |B|^2 + 2|A||B|cosθ ...(1)
|A-B|^2 = |A|^2 + |B|^2 + 2|A||B|cos(180-θ) ...(2)

From (1) & (2),
cosθ = cos(180-θ)
θ = 180-θ
2θ = 180
θ = 90°

Hence, angle between A and B is 90°.

Hope that is helpful...