# How do I find the magnitude and direction angle of the vector v=3i- 4j?

Jun 4, 2015

The vector is a plane vector (only $i$ and $j$)

Now the magnitude is easy (Pythagoras):
${m}_{v}^{2} = {3}^{2} + {\left(- 4\right)}^{2} = 25 \to {m}_{v} = 5$

As for the angle :
The tangent of the angle is $\frac{3}{-} 4$

Use the ${\tan}^{-} 1 \left(- 0.75\right)$ function to get $- {36.87}^{o}$
(you can add ${360}^{o}$ to get ${323.13}^{o}$)