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 $5\ \mathrm{m}$ to the right is +$5\ \mathrm{m}$, and $3\ \mathrm{m}$ to the left is $-3\ \mathrm{m}$. A force works the same way: a pull of $2\ \mathrm{N}$ to the left is $-2\ \mathrm{N}$.

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.