Question

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

Answer 1

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`)