vectors- 2 ways to describe them?

Question

ordered pair and componet form, what the difference?

Answer 1

Eh...usually the 2 ways are specified as component form and magnitude/direction...

But this is a vector in component form:

u = 3i + 4j

(where i is the unit vector in the positive x direction, and j is the unit vector in the positive y direction).

In ordered pair form, I think it would be almost the same thing:

(3, 4) or my preferred way, <3, 4> (which shows it's not a point).

The other way is magnitude and direction. The magnitude is the square root of the sum of the squares (Pythagorean theorem), and the direction is the arctangent of the y component over the x-component.

So that same vector would be:

magnitude = 5, direction = arctan(4/3)