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

Explanation

Let the two vectors be `vec A and vec B` . As the vectors
` (vec A + vec B) and (vec A-vec B) are perpendicular to each other so their dot product is zero. i.e.,
` ( vec A + vec B) . ( vec A- vec B) =0`
or ` vec A. vec A- vec A. vec B= vec B. vec A- vec B. vec B=0`
(:. vec A. vec B= vec B. vec A)`
or ` A^2 -B^2 =0 or A^2 = B^2 or A= B`.