Find the Angle Between the Vectors $\mathbf { u }$ And $\mathbf { v }$

question 26

Multiple Choice

Find the angle between the vectors $\mathbf { u }$ and $\mathbf { v }$ .
$$\mathbf { u } = \cos \left( \frac { \pi } { 3 } \right) \mathbf { i } + \sin \left( \frac { \pi } { 3 } \right) \mathbf { j } , \mathbf { v } = \cos \left( \frac { 5 \pi } { 4 } \right) \mathbf { i } + \sin \left( \frac { 5 \pi } { 4 } \right) \mathbf { j }$$

• A) \(40 ^ { \circ }\)
• B) \(75 ^ { \circ }\)
• C) \(105 ^ { \circ }\)
• D) \(165 ^ { \circ }\)
• E) \(175 ^ { \circ }\)

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Definitions:

Expected Value

The long-run average value of repetitions of the same experiment or random trial, indicating the central tendency.

Random Variable

A variable that can take on numerical results from a random event or experiment.

Standard Deviation

An indicator of the spread of a dataset relative to its mean, used to quantify the degree to which individual data points differ from the average.

Monthly Production

The total output or production of a manufacturing process or facility in a single month.