Understanding vectors involves grasping that they have both a quantity and a direction. Learn to use appropriate symbols to represent vectors quantities. By subtracting the coordinates of one point from another, we can uncover the components of a vector. Vectors can be used to solve problems related to velocity and other similar quantities. Adding vectors can be achieved end-to-end, component-wise or via the parallelogram rule; just remember that the sum of two vectors' magnitudes is not the same as the combined magnitude of two vectors.

Knowing two vectors' magnitude and direction enables us to figure out the sum of their magnitude and direction. Interpreting vector subtraction is done as v + (–w), where –w is the additive inverse of w; subtract vectors graphically by connecting tips in the right sequence and do this component-wise. Showing scalar multiplication graphically can be done by adjusting the vectors' scale and possibly their direction then performing scalar multiplication component-wise. Once the magnitude of scalar multiple cv has been calculated using ||cv|| = |c|v, the direction of cv can be uncovered, provided that |c|v ≠ 0.

Matrices can be used to arrange and manipulate data. They can be multiplied by scal