How do I write a vector in component form and then convert it into magnitude and direction?

Question

What steps do I take to solve this? Example?

Answer 1

I assume that "component form" means the vector is described using x and y coordinates (on a standard graph, where x and y are orthogonal)

The magnitude (M) of the vector is obtained using the Pythagorean Theorem:

M^2 = x^2 + y^2

The angle (A) is the inverse tangent of x/y: A = atan (x/y)

Sketch the vector on graph paper to get the correct angle. For example, if x/y = +1, the angle is either +45 or -135