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

Image Transcription

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

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Advanced Math

Vector Spaces