The sum and difference of two vectors are perpendicular to each other.

1.	The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.
Answer» As the vector \(\vec A+\vec B \) and \(\vec A-\vec B\) are perpendicular to each other, therefore \((\vec A+\vec B).(\vec A-\vec B)=0\) \(\vec A.\vec A-\vec A.\vec B+\vec B.\vec A-\vec B.\vec B=0\) or A² - B² = 0 A = B (∵ \(\vec A.\vec B=\vec B.\vec A\))

The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.

Answer»

As the vector \(\vec A+\vec B \) and \(\vec A-\vec B\) are perpendicular to each other, therefore

\((\vec A+\vec B).(\vec A-\vec B)=0\)

\(\vec A.\vec A-\vec A.\vec B+\vec B.\vec A-\vec B.\vec B=0\)

or A² - B² = 0

A = B (∵ \(\vec A.\vec B=\vec B.\vec A\))

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The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.

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