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.
