Axes and Directions

To describe a vector with numbers, pick axes: two lines at right angles, x and y. Each axis has a positive direction, marked by its arrowhead.

With +x to the right: right is +, left is −.

A vector along an axis gets a sign: + when it points the positive way, − when it points the other way. With +x to the right, a displacement of 5 m to the right is +5 m, and 3 m to the left is −3 m. A force works the same way: a pull of 2 N to the left is −2 N.

You choose the axes. Any two lines at right angles work, but one choice makes the work easy: put one axis along the line the object moves on. On a ramp, tilt the axes with the slope.

On a ramp the axes tilt with the slope: x along it, y at right angles.

On the board. In a physics challenge the Axes step draws a cross on the picture. Turn 15° rotates it, Flip +x and Flip +y change which way is positive. Line one axis up with the motion, then press Check.