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) \(\begin{array} { l }
• \mathbf { u } \times \mathbf { v } = 8 \mathbf { i } - 8 \mathbf { j } \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = 0 \\
• ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { v } = 0
• \end{array}\)

Understanding of key financial ratios and their calculations.

Ability to analyze a company's financial performance based on provided data.

Proficiency in calculating a company's market-based ratios (e.g., price-earnings ratio, dividend yield).

Skill in assessing a company's liquidity through working capital, current ratio, and acid-test ratio.

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Definitions:

Short Run

A period in which at least one input, such as plant size or capital, is fixed and cannot be varied to change output levels.

Long Run

A time frame in economics where all inputs and costs are variable, allowing for full adjustment to changes.

Peak Efficiency

The maximum performance level at which a system, process, or machine operates with optimal effectiveness and minimal waste.

Break-Even Point

The level of production or the volume of sales at which total costs equal total revenue, meaning there is no profit or loss.