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

Question

56473 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-04T20:53:48

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

Now the magnitude is easy (Pythagoras):
$m_v ^2=3^2+(-4)^2=25-> m_v=5$

As for the angle :
The tangent of the angle is $3/-4$

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

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