Question

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0, 360°].

Answer 1

magnitude = 8.5

direction angle = 45°

To get the magnitude of a vector , we will use the following formula:

`||\vec{u}||=√(a^2+b^2)`

Substituting a = 6 and b =6:

`\begin{gathered} ||\vec{u}||=√(a^2+b^2) \\ ||\vec{u}||=√(6^2+6^2) \\ ||\vec{u}||=√(36+36) \\ ||\vec{u}||=√(72) \\ ||\vec{u}||=8.485\approx8.5 \end{gathered}`

For the direction angle, we will use the following formula:

`\begin{gathered} \tan\theta=(b)/(a) \\ \theta=\tan^(-1)(6)/(6) \\ \theta=45 \end{gathered}`

The magnitude is 8.5 while the direction angle is 45°