Determine whether the statement below is true or false. Justify the nswer. The vector is in Rn. if || u ||^2 + || v ||^2 = || u + v ||^2, then u and v are orthogonal. A. The statement is true. By the Pythagoreanâ 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||^2â, then u and v are orthogonal complements.
C. The statement is false. Two vectors u and v are orthogonal if uâ¢v=0. If ||u||^2+ ||v||^2= ||u+v||^2â, then uâ¢v=1.
D. The statement is true. By the definition of the innerâ product, two vectors u and v are orthogonal if and only if ||u+v||^2= ||u||^2+ ||v||^2.