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

question 173

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

---

Definitions:

Price

The amount of money required to purchase a good or service, determined by factors such as supply and demand, production costs, and market competition.

Coal Miners

Individuals and companies engaged in the extraction of coal from the earth.

Environmental Laws

Regulations and standards aimed at preserving and protecting the environment from harmful practices or pollutants, promoting sustainability.

Oil

A natural fossil fuel that is used primarily for energy production and as a raw material in manufacturing.