1.4.2—Add and subtract coplanar vectors

To add vectors, place the tail of one at the head of the other; the resultant joins the first tail to the final head. In components, add corresponding horizontal and vertical parts.

Preserve direction and scale in diagrams, then use Pythagoras or trigonometry only after resolving or forming the correct triangle.

Vectors (3,4) and (−1,2) add to (2,6), whose magnitude is √40.

Adding magnitudes ignores angle; opposite vectors can cancel even when each has a large magnitude.