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Find the direction angle of the vector v=-5i-7j That is, find the angle between 0 and 360 that v makes with the positive x-axis (measured counterclockwise), when v is in standard position. Do not round any intermediate computations, and round your answer to the nearest whole number.

Find the direction angle of the vector v5i7j That is find the angle between 0 and 360 that v makes with the positive xaxis measured counterclockwise when v is i class=

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Answer:

234 degrees.

Explanation:

Given a vector, v=, the direction of the vector is found using the formula below:

[tex]\theta=\arctan (\frac{b}{a})[/tex]

Given the vector: v=-5i-7j

[tex]\begin{gathered} a=-5,b=-7 \\ \implies\theta=\arctan (\frac{-7}{-5})=54.46\degree \end{gathered}[/tex]

However, note that both coordinates are negative, thus, the angle is in the third quadrant,

Therefore, the direction angle of vector v will be:

[tex]180+\theta=180+54.46=234.46\degree\approx234\degree[/tex]

Rounded to the nearest whole number, the angle is 234 degrees.

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