Find the Component Form of Vector $\mathbf { u } + \mathbf { v } \text { given } \| \mathbf { u } \| = 2 \text { and } \| \mathbf { v } \| = 3 \text { and the angles }$

question 85

Multiple Choice

Find the component form of vector $\mathbf { u } + \mathbf { v } \text { given } \| \mathbf { u } \| = 2 \text { and } \| \mathbf { v } \| = 3 \text { and the angles }$ that $\mathbf { u }$ and $\mathbf { v }$ make with the positive $x$ -axis are $\theta _ { \mathbf { u } } = 0 ^ { \circ }$ and $\theta _ { \mathbf { v } } = 45 ^ { \circ }$ .

• A) \(\left( \frac { 4 + 3 \sqrt { 3 } } { 2 } , \frac { 9 \sqrt { 2 } } { 2 } \right)\)
• B)\(\left( \frac { 2 + 3 \sqrt { 2 } } { 2 } , \frac { 9 \sqrt { 2 } } { 2 } \right)\)
• C)\(\left\{ \frac { 22 + 9 \sqrt { 2 } } { 2 } , \frac { 6 \sqrt { 2 } } { 2 } \right\}\)
• D)\(\left( \frac { 4 + 3 \sqrt { 2 } } { 2 } , \frac { 3 \sqrt { 2 } } { 2 } \right)\)
• E)\(\left( \frac { 2 + 9 \sqrt { 2 } } { 2 } , \frac { 9 \sqrt { 2 } } { 2 } \right)\)

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Definitions:

Inferential Statistics

Statistical methods that allow researchers to make inferences or generalizations about a population based on a sample.

Representative Sample

A subset of a population that accurately reflects the members of the entire population.

Effect Size

A quantitative measure of the magnitude of a phenomenon, used to indicate the size of an experimental effect.

Independent Variable

The variable in an experiment that is manipulated or changed to observe its effect on the dependent variable.