Addition and Subtraction of Vectors

Only vectors describing the SAME physical quantity can be added or subtracted — for instance, two forces $\vec F_1$ and $\vec F_2$ can be combined into a resultant force $\vec F = \vec F_1+\vec F_2$, but a force vector can never be added to a velocity vector, since they are different physical quantities.

When two vectors of the same type act along the same line, their addition is straightforward:

Parallel vectors (same direction): if $\vec{AB}$ and $\vec{BC}$ point the same way, the magnitude of the resultant is the sum of the individual magnitudes, $AC = AB + BC$, and the direction of the resultant is the same as that of the individual vectors.

Anti-parallel vectors (opposite directions): the magnitude of the resultant is the DIFFERENCE of the individual magnitudes, $AC = AB - BC$, and the direction of the resultant is that of the LARGER of the two vectors. …