Find U × V and Show That It Is Orthogonal $\mathbf { u } = ( 6 , - 1,7 ) \quad \mathbf { v } = ( 5,5 , - 1 )$

question 48

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $\mathbf { u } = ( 6 , - 1,7 ) \quad \mathbf { v } = ( 5,5 , - 1 )$

• A) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( 34,41,35 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• B) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( - 34,41,35 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• C) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( 41,34,35 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } \neq 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } \neq 0
• \end{array}\)
• D) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( - 35,41,34 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• E) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = ( - 41,41,35 ) \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)

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Definitions:

Main Connective

The main connective in a logical expression is the operator that determines the truth value of the entire expression, generally by combining the truth values of its component parts.

Symbolize

To represent or stand for something else, often an abstract idea, by means of symbols.

Main Connective

The logical operator in a compound proposition that determines the proposition's overall truth value.

Truth Table

A table used in logic to determine the validity of a proposition by listing all possible scenarios and their corresponding truth values.