Determine whether the statement below is true or false. Justify the answer. The vectors are in R". If Ju|? + |v| = ||u +v|l°, 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 =D В. The statement is false. If ||u|| + ||v| = ||u + v||, then u and v are orthogonal complements. с. 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|. D. The statement is false. Two vectors are orthogonal if u · v = 0. If |lu|? + ||v|? = |u + v|?, then u - v = 1. and %3D O O O O

Question

Determine whether the statement below is true or false. Justify the answer. The vectors are in Rn. If (see picture), then u and v are orthogonal.

Determine whether the statement below is true or false. Justify the answer. The vectors are in R".
If Ju|? + |v| = ||u +v|l°, 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
=D
В.
The statement is false. If ||u|| + ||v| = ||u + v||, then u and v are orthogonal complements.
с.
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|.
D.
The statement is false. Two vectors
are orthogonal if u · v = 0. If |lu|? + ||v|? = |u + v|?, then u - v = 1.
and
%3D
O O O O
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Transcribed Image Text

Determine whether the statement below is true or false. Justify the answer. The vectors are in R". If Ju|? + |v| = ||u +v|l°, 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 =D В. The statement is false. If ||u|| + ||v| = ||u + v||, then u and v are orthogonal complements. с. 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|. D. The statement is false. Two vectors are orthogonal if u · v = 0. If |lu|? + ||v|? = |u + v|?, then u - v = 1. and %3D O O O O