Find U × V and Show That It Is Orthogonal $\begin{array} { l } \mathbf { u } = - \mathbf { i } + \mathbf { k } \\\mathbf { v } = \mathbf { j } - 3 \mathbf { k }\end{array}$

question 139

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $\begin{array} { l } \mathbf { u } = - \mathbf { i } + \mathbf { k } \\\mathbf { v } = \mathbf { j } - 3 \mathbf { k }\end{array}$

• A) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = \mathbf { i } - 3 \mathbf { j } - \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• B) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - \mathbf { i } - 3 \mathbf { j } - \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• C) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - \mathbf { i } + 3 \mathbf { j } - \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• D) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - \mathbf { i } - 3 \mathbf { j } + \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• E) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = \mathbf { i } - 3 \mathbf { j } + \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)

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Definitions:

Scatterplot

A graphical representation of data points plotted on a horizontal and vertical axis to visualize the relationship between two variables.

Dependent Variable

The variable in a study that is anticipated to vary as a result of changes made to the independent variable.

Correlation Coefficient

A numerical measure that assesses the strength and direction of a linear relationship between two quantitative variables.

Covariance Value

A measure indicating the extent to which two variables change together, showing if increases in one variable correspond to increases in another.