Find U × V and Show That It Is Orthogonal

question 147

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $$\begin{array} { l } \mathbf { u } = 12 \mathbf { i } + 6 \mathbf { j } + \mathbf { k } \\\mathbf { v } = \mathbf { i } + 5 \mathbf { j } - 6 \mathbf { k }\end{array}$$

• A) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = 73 \mathbf { i } - 41 \mathbf { j } - 41 \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• B) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = 73 \mathbf { i } - 41 \mathbf { j } + 73 \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• C) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = 73 \mathbf { i } - 41 \mathbf { j } + 54 \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• D) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - 41 \mathbf { i } + 73 \mathbf { j } + 54 \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• E) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - 41 \mathbf { i } + 73 \mathbf { j } - 41 \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)

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