Determine whether the statement below is true or false. Justify the answer. The vectors are in

ℝn. If ||u||^2+||v||^2=||u+v||^2​, then u and v are orthogonal.

Choose the correct answer below.

A.The statement is true. By the Pythagorean​ Theorem, two vectors u and v are orthogonal if and only if ||u+v||^2=||u||2+||v||2.

B.The statement is false. If ||u||^2+||v||^2= ||u+v||^2​, then u and v are orthogonal complements.

C.The statement is false. Two vectors u and v are orthogonal if u•v=0. If ||u||^2+ ||v||^2= ||u+v||^2​, then

u•v=1.

D.The statement is true. By the definition of the inner​ product, two vectors u and v are orthogonal if and only if

||u+v||^2= ||u||^2+ ||v||^2.