Question

Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.

Answer 1

Recall that the magnitude and direction of a vector:

`\vec{v}=ai+bj`

are given by the following formulas:

`\begin{gathered} \vec|=√(a^2+b^2), \\ \theta=tan^(-1)((b)/(a)). \end{gathered}`

Substituting

`\begin{gathered} a=2, \\ b=8, \end{gathered}`

in the above formulas, we get:

`\begin{gathered} \vecv|=√(2^2+8^2)=√(4+64)=√(68). \\ \theta=\tan^(-1)((8)/(2))=\tan^(-1)(4). \end{gathered}`

Finally, we get:

`\begin{gathered} \vec|=2√(17), \\ \theta=75.9638^(\circ). \end{gathered}`

Answer: (|v|=2√17, θ=75.9638°)