Question

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

Answer 1

Dear Student ,

Let's consider the following cross product

(A + B) X (A - B)

if the two ar mutually perpendicular then Cosα (where α is the angle between them) would be zero

so,

(A + B) X (A - B) = 0

thus

(A X A) - (B X B) - (A X B) + (B X A) = 0

or

A² - B² = 0 ( A X B = - B X A )

thus, we get

A = B

or

A = B

so the two vectors are equal in magnitude.
Regards