 Now that we've looked at position in one dimension and we have vectors, we can look at position in two dimensions. So reviewing real quick position in one dimension, that was motion or position along a line. So we had either horizontal positions or we had vertical positions, but we only had one of those two cases. Either case was a vector because it mattered whether I was positive or negative. They had dimensions of type length, which means I had a standard unit of meters. In two dimensions, we have x and y at the same time. In polar coordinates, we have our r and theta, which represented our x and y, but r is the magnitude and theta is my direction. So using our standard vector notation, we can write our full position vector as r with the vector sign over it. And it has the two components x and y, so that becomes r vector is x i hat plus y j hat. The magnitude then is how long it is, and that uses our symbols with our absolute value signs for the r, and that's the square root of x squared plus y squared. If my direction is measured relative to the positive x-axis, our standard polar coordinate type direction, then theta is the inverse cosine of y over x. Graphically, this represents our basic trigonometric triangle. x and y are our components of the vector, r the length of the vector is the hypotenuse, and my angle again theta was measured up from the positive x-axis. So I'm going counterclockwise. Remember that I can also think of my vector as having the components of the projections out onto the x and y-axis, so I could represent graphically the vector this way as well. That gives us our overview of position in two dimensions.