Vectors basics
A vector represents a quantity with both size and direction, like velocity or force, and is written as an ordered pair or triple of components, such as <3, 4>, or drawn as an arrow. You add vectors by adding their matching components, like <3, 4> + <1, 2> = <4, 6>, and multiply a vector by a scalar (a plain number) by multiplying every component, like 2 x <3, 4> = <6, 8>, which stretches or shrinks the vector without changing its direction, or reverses it if the scalar is negative; a vector's magnitude, its length, comes from the Pythagorean theorem applied to its components: for <3, 4>, that's the square root of 3^2 + 4^2 = 25, which is 5.
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