# Vectors and Scalars

#### AnthreX

whats the difference between

Vectors and Scalars

thanx

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#### HallsofIvy

Homework Helper
Open a book on vectors and read the definitions!

I'm not (just) being facetious. There are several different ways of looking at, and thinking about, vectors and the answer to your question depends upon which one you mean.

In the simplest sense (what I think of as the "Physics" definition) vectors are things that have both a numerical value and a "direction". Scalars are simply numbers. One defines "scalar multiplication", multiplying a scalar by a vector, as multiplying the numerical value of the vector by the scalar (so we are multiplying a number by a number) while leaving the direction of the vector unchanged.

That's probably the definition you want.

ohhh i c...

thanx

#### SmarterThanGod

Scalars are magnitude
Vectors are magnitude AND direction.
The major difference is how they are added and subtracted, but thats another story......

#### BigRedDot

Vectors are magnitude AND direction.
The notion of vector really encompasses much, much more than this. Essentially, vectors are any mathematical objects that can be combined linearly to still produce more of the same kind of objects. That so, there are plenty of examples of vectors that don't present any notion of "direction" (or even "magnitude" -- not all vector spaces have norms.) The space of continuous functions on the interval [-1,1] is a vector space, but it would be hard to say that the functions that comprise it have a "magnitude and direction."