The Vector

A vector has direction and magnitude.

Well, technically, anything that fulfils the criteria of a vector space is a vector.

is the set of all vectors with components, each of which is a real number.

It all the components of and are equal, then

is a zero vector, and all it's components are

Vectors can be added by adding their components

Vector components are all multiplied by a scalar value

Two nonzero vectors are parallel if they are scalar multiples of each other

Two lines in are parallel if their direction Vectors are parallel. Two Planes in are parallel if their normal vectors are parallel

Two or more vectors whose respective components are multiplied, and then added with each other.

Let and for some positive integer

is a linear combination of the vectors .