Question

Given vector u equals 30 (cos 60 degrees, sin 60) what are the magnitude and direction of −4u?

Answer 1

Magnitude is -120 and the direction is 60°

Explanation:

The unit vector is:

`u=30\langle\cos60\degree,\sin60\degree\rangle`

Let's call the new vector v, which would be:

v = -4u

The magnitude is calculated as follows:

`\begin{gathered} ||u||=30\cdot√(\left(cos\:60\right)^2+\left(sin\:60\right)^2)=30 \\ ||v||=-4\cdot||u||=-4\cdot30=-120 \\ ||v||=-120 \end{gathered}`

For the direction:

`\begin{gathered} \tan\theta=(-120\cdot\sin60)/(-120\cdot\cos60)=((√(3))/(2))/((1)/(2)) \\ \tan\theta=√(3) \\ \theta=\tan^(-1)(√(3)) \\ \theta=60\degree \end{gathered}`

Which means that the magnitude is -120 and the direction is 60°