Find U × V and Show That It Is Orthogonal $\begin{array} { l } \mathbf { u } = 8 \mathbf { k } \\\mathbf { v } = - \mathbf { i } + 4 \mathbf { j } + \mathbf { k }\end{array}$

question 4

Multiple Choice

Find u × v and show that it is orthogonal to both u and v. $\begin{array} { l } \mathbf { u } = 8 \mathbf { k } \\\mathbf { v } = - \mathbf { i } + 4 \mathbf { j } + \mathbf { k }\end{array}$

• A) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = 4 \mathbf { i } - 8 \mathbf { j } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• B) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - 32 \mathbf { i } - 8 \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• C) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - 32 \mathbf { i } - 8 \mathbf { j } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• D) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = - 32 \mathbf { j } - 8 \mathbf { k } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)
• E) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = 8 \mathbf { i } - 8 \mathbf { j } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)

---

Definitions:

SST

Sum of Squares Total, a measure used in statistical analysis that quantifies the total variation within a dataset.

Independent Variable

In an experimental setup, it's the factor that is intentionally manipulated to measure its impact on the dependent variable.

Multiple Regression Model

An analytical approach that connects a dependent variable with two or more independent variables.

Multiple Regression Analysis

A statistical technique that models the relationship between a dependent variable and two or more independent variables by fitting a linear equation to observed data.