The displacement, force, velocity, and acceleration vectors’ components are given. Calculate the magnitude and direction of each vector. (a) x = +15.0 cm, y = -12.3 cm.

Question

I am completely lost.

Answer 1

The magnitude |<x,y>| of a vector given as <x,y> can be obtained by a calculation similar to Pythagoras theorem. For example,
|<3,4>| = sqrt(3²+4²)=5
The direction θ with respect to the x-axis can be calculated using a calculator by:
θ=tan^-1(y/x)
but add 180° if x is negative.
For example, for <-12,5>
θ=tan^-1(-12/5)
=tan^-1-67.4°
But since x<0, we add 180° to give
θ=112.6°

You can use the same procedure to calculate the magnitude and direction of all vectors when the x,y components are given.