Vectors are an extremely enormously useful geometric object in maths and physics. Vectors express a direction and a magnitude (or length), in both 2D and 3D space. Vectors are key concept not only for producing geometry through code, but also for motion and interactive animation.
(Diagram 1. Euclidean vector)
The direction of a vector is simply represented with an arrow, with the length of the arrow expressing the magnitude. The information to create a 2D vector can be easily recorded with just two numbers, which can be negative or positive.
a = ( 3, 6 )
(Diagram 2. vector a)
The key thing to remember is that vectors represent direction and magnitude without a location. For this reason vectors are often combined with a coordinate. Confusingly, 2D and 3D coordinates are generally recorded in the same format as vectors, with just two numbers. However, coordinates are normally visually represented as points.
(Diagram 3. vector a, translated to point b (5,3)
There are a number of ways to manipulate and combine vectors with simple operations (vector maths).
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a = ( 3, 6)
b = ( 6, -3 )
a + b = (9, 3)
(Diagram 4. vector addition)
Subtraction
Subtracting two vectors
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