AI Tutor
If you walk 4 meters east, then turn and walk 3 meters north, your odometer reads 7 meters — but you are actually only 5 meters from where you started.
Because physical quantities like displacement, velocity, and force have direction, adding them requires a visual geometry rule called vector addition.

Anatomy of a Vector

A vector is an arrow representing a quantity with both size (magnitude) and direction. The base where the arrow begins is called the tail, and the pointy end is called the tip (or head).
What happens when you combine two different vector arrows acting on the same object?

The Tip-to-Tail Method

To add vectors graphically, place the tail of the second vector directly at the tip of the first vector, keeping both vectors' lengths and angles unchanged.
The combined effect is the resultant vector (R⃗\vec{R}), drawn as a new arrow starting at the very first tail and pointing straight to the very last tip.
In 1586, Flemish mathematician Simon Stevin first discovered this geometric rule while analyzing how hanging ropes combine forces to balance heavy weights.
Does the order in which you chain the vectors change where you end up?

Order Does Not Matter