Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Finding the magnitude and angle from the components

Given that the Δr vector from LA to Las Vegas has Δx = 290 km and Δy = 230 km, how would we find the magnitude and direction of Δr?

We find the magnitude of Δr from the Pythagorean theorem:

We know all three sides of the triangle, so the angle θ can be found using any of the inverse trig functions. For example, we know the opposite and adjacent sides, so

Last Update: 2010-11-11