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Question

If a+b=ab, then prove that a and b are mutually perpendicular vectors.

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Solution

|a+b|=|ab| Let θ be angle between them
|a+b|2=|ab|2
|a|2+|b|22|a||b|cosθ=|a|2+|b|2+2|a||b|cosθ
2|a||b|cosθ=2|a||b|cosθ.
cosθ=0.cosθ
θ=π2
Vectors are mutually perpendicular.

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