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• (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and c are parallel. • (e) Suppose a, b, c are non-zero vectors in R4, and a is perpendicular to both of b, c. Then b and c are parallel.

• (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and c are parallel. • (e) Suppose a, b, c are non-zero vectors in R4, and a is perpendicular to both of b, c. Then b and c are parallel.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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True or False. Explanations are required. 

### Vector Perpendicularity and Parallelism In this section, we will explore the relationships between vectors in different dimensional spaces, specifically focusing on perpendicularity and parallelism. #### (d) Perpendicular and Parallel Vectors in \(\mathbb{R}^2\) - **Statement:** Suppose \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non-zero vectors in \(\mathbb{R}^2\), and \(\mathbf{a}\) is perpendicular to both \(\mathbf{b}\) and \(\mathbf{c}\). Then \(\mathbf{b}\) and \(\mathbf{c}\) are parallel. #### (e) Perpendicular and Parallel Vectors in \(\mathbb{R}^4\) - **Statement:** Suppose \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non-zero vectors in \(\mathbb{R}^4\), and \(\mathbf{a}\) is perpendicular to both \(\mathbf{b}\) and \(\mathbf{c}\). Then \(\mathbf{b}\) and \(\mathbf{c}\) are parallel.
Transcribed Image Text:### Vector Perpendicularity and Parallelism In this section, we will explore the relationships between vectors in different dimensional spaces, specifically focusing on perpendicularity and parallelism. #### (d) Perpendicular and Parallel Vectors in \(\mathbb{R}^2\) - **Statement:** Suppose \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non-zero vectors in \(\mathbb{R}^2\), and \(\mathbf{a}\) is perpendicular to both \(\mathbf{b}\) and \(\mathbf{c}\). Then \(\mathbf{b}\) and \(\mathbf{c}\) are parallel. #### (e) Perpendicular and Parallel Vectors in \(\mathbb{R}^4\) - **Statement:** Suppose \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non-zero vectors in \(\mathbb{R}^4\), and \(\mathbf{a}\) is perpendicular to both \(\mathbf{b}\) and \(\mathbf{c}\). Then \(\mathbf{b}\) and \(\mathbf{c}\) are parallel.
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