Question

If the component form of a vector is <5,-2>,which of the following is the correct determination of the direction angle in the interval [0 degrees, 360 degrees)?

Answer 1

Given:

`v=<5,-2>`

To Determine: The direction angle in the interval [0 degree, 360 degrees)

Solution

Given

`\begin{gathered} \\ \theta=tan^(-1)((y)/(x)) \end{gathered}`

Substitute

Note that the vector is in the fourth quadrant

`\begin{gathered} \theta=tan^(-1)(-(2)/(5)) \\ \theta=tan^(-1)(-0.4) \\ \theta=-(21.80^0) \\ \theta=360-21.80 \\ \theta=338.20^0 \end{gathered}`

Hence, the direction angle is 338.20⁰