Find the Unit Vector in the Direction of the Given $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$

question 19

Multiple Choice

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.
-Let $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ . Find the unit vector in the direction of $\mathbf { u }$ , and write your answer as a linear combination of the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$ .

• A) \(\frac { - 3 } { \sqrt { 13 } } \mathrm { i } + \frac { 2 } { \sqrt { 13 } } \mathrm { j }\)
• B) \(- \frac { 3 } { 13 } i - \frac { 2 } { 13 } j\)
• C) \(\frac { - 3 } { \sqrt { 13 } } \mathrm { i } - \frac { 2 } { \sqrt { 13 } } \mathrm { j }\)
• D) \(- \frac { 3 } { 5 } i - \frac { 2 } { 5 } j\)

Determine the impact of altering resource availability on the optimal solution and overall profit.

Comprehend and calculate labor and production requirements and constraints within given scenarios.

Understand the concept of shadow prices and their relevance in sensitivity analysis.

Interpret Solver output messages to diagnose model feasibility and solution characteristics.

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Definitions:

Flexible Budget

A budget that adjusts or varies with changes in the volume of activity or other relevant factors, helping managers to better allocate resources.

Variable Manufacturing Overhead

Costs in manufacturing that vary with the level of production output, such as electricity for machinery.

Variable Overhead Rate Variance

The difference between the actual variable overhead cost incurred during a period and the standard cost that should have been incurred based on the actual activity of the period.

Direct Labor-Hours

A measure of the total hours worked by employees directly involved in manufacturing a product or providing a service.