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Scalar Multiplication

Vectors can be multiplied by a scalar (a number).     If v is a vector, and c is a number,

then c · v is the vector with the same direction as v but c times the size.

So for example if F represents a force, then 2F represents a doubling of the size of the force, keeping the direction the same.

Similarly -3F represents a tripling of the size of the force, going in the opposite direction to the original force.

In terms of coordinates this means:

If v = [v1, v2, v3, ..., vn], then c · v = [cv1, cv2, ..., cvn].

For example:
5 ·[-2,10] = [- 10, 50], (-3) ·[2,3,- 4] = [- 6,- 9,12]
Properties of scalar multiplication, valid for any v and any scalars a and b:
0v-= 0, 1v-= v, (- 1)v = - v, (- a)v-= - (av), (ab)v = a(bv), |av| = |a||v|.

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