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Determine whether the following vectors are mutually orthogonal. U₁ = (1, -6, 1), U₂ = (0, 1, 6), u3 = (-37, -6, 1) Is the set of vectors orthogonal? .. OA. The vectors are not mutually orthogonal because u₁ is not orthogonal to u3. OB. The vectors are mutually orthogonal because each pair of distinct vectors is orthogonal. OC. The set of vectors is orthogonal because u₁ is orthogonal to u₂ and u₂ is orthogonal to u3.

Determine whether the following vectors are mutually orthogonal. U₁ = (1, -6, 1), U₂ = (0, 1, 6), u3 = (-37, -6, 1) Is the set of vectors orthogonal? .. OA. The vectors are not mutually orthogonal because u₁ is not orthogonal to u3. OB. The vectors are mutually orthogonal because each pair of distinct vectors is orthogonal. OC. The set of vectors is orthogonal because u₁ is orthogonal to u₂ and u₂ is orthogonal to u3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Determining Orthogonality of Vectors **Problem Statement:** Determine whether the following vectors are mutually orthogonal. Given Vectors: - \( \mathbf{u}_1 = (1, -6, 1) \) - \( \mathbf{u}_2 = (0, 1, 6) \) - \( \mathbf{u}_3 = (-37, -6, 1) \) **Question:** Is the set of vectors orthogonal? **Answer Choices:** - **A.** The vectors are not mutually orthogonal because \( \mathbf{u}_1 \) is not orthogonal to \( \mathbf{u}_3 \). - **B.** The vectors are mutually orthogonal because each pair of distinct vectors is orthogonal. - **C.** The set of vectors is orthogonal because \( \mathbf{u}_1 \) is orthogonal to \( \mathbf{u}_2 \) and \( \mathbf{u}_2 \) is orthogonal to \( \mathbf{u}_3 \). - **D.** The vectors are not mutually orthogonal because \( \mathbf{u}_2 \) is not orthogonal to \( \mathbf{u}_3 \). - **E.** The vectors are mutually orthogonal because the vectors are linearly independent. - **F.** The vectors are not mutually orthogonal because \( \mathbf{u}_1 \) is not orthogonal to \( \mathbf{u}_2 \).
Transcribed Image Text:### Determining Orthogonality of Vectors **Problem Statement:** Determine whether the following vectors are mutually orthogonal. Given Vectors: - \( \mathbf{u}_1 = (1, -6, 1) \) - \( \mathbf{u}_2 = (0, 1, 6) \) - \( \mathbf{u}_3 = (-37, -6, 1) \) **Question:** Is the set of vectors orthogonal? **Answer Choices:** - **A.** The vectors are not mutually orthogonal because \( \mathbf{u}_1 \) is not orthogonal to \( \mathbf{u}_3 \). - **B.** The vectors are mutually orthogonal because each pair of distinct vectors is orthogonal. - **C.** The set of vectors is orthogonal because \( \mathbf{u}_1 \) is orthogonal to \( \mathbf{u}_2 \) and \( \mathbf{u}_2 \) is orthogonal to \( \mathbf{u}_3 \). - **D.** The vectors are not mutually orthogonal because \( \mathbf{u}_2 \) is not orthogonal to \( \mathbf{u}_3 \). - **E.** The vectors are mutually orthogonal because the vectors are linearly independent. - **F.** The vectors are not mutually orthogonal because \( \mathbf{u}_1 \) is not orthogonal to \( \mathbf{u}_2 \).
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