If $\| \mathbf { u } \| = 5$ And $\| \mathbf { v } \| = 3$

question 24

Multiple Choice

If $\| \mathbf { u } \| = 5$ and $\| \mathbf { v } \| = 3$ , and the vectors make angles of $150 ^ { \circ }$ and $110 ^ { \circ }$ with the $x$ -axis respectively, find the component form of the sum of $\mathbf { u }$ and $\mathbf { v }$ . Round answers to two decimal places.

• A) \(\langle - 5.36,5.32 \rangle\)
• B) \(\langle - 3.30 , - 0.32 \rangle\)
• C) \(\langle 1.47 , - 1.51 \rangle\)
• D) \(\langle 3.53 , - 7.15 \rangle\)
• E) \(\langle - 4.31,6.20 \rangle\)

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Definitions:

Critical Value

A threshold in hypothesis testing that defines the boundary or cutoff for deciding whether to reject the null hypothesis.

Null Hypothesis

A statistical hypothesis that suggests there is no effect or no difference, and it serves as the default position that there is no association between two measured phenomena.

One-way ANOVA

A statistical method used to compare the means of three or more independent groups to determine if there is a statistically significant difference among them.

F-ratio

The F-ratio is a statistic used in analysis of variance (ANOVA) to compare the variability between groups to the variability within groups, assessing whether group means are significantly different.