Find U × V and Show That It Is Orthogonal $\mathbf { u } = ( 10,0,3 ) \quad \mathbf { v } = ( 10,0,0 )$

question 242

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $\mathbf { u } = ( 10,0,3 ) \quad \mathbf { v } = ( 10,0,0 )$

• A) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( 0,30,0 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• B) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( 0 , - 30,0 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• C) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( 0,30,0 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0
• \end{array}\)
• D) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( 30,0,0 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• E) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( 0,0,30 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0
• \end{array}\)

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