Multiplication is like repeated addition. Multiplying 4 by 3 means adding four three times:
. The multiplication of a vector times a scalar works in the same way. Multiplying the vector
A by the positive scalar
c is equivalent to adding together
c copies of the vector
A. Thus 3
A =
A +
A +
A. Multiplying a vector by a scalar will get you a vector with the same direction, but different magnitude, as the original.
The result of multiplying
A by
c is a vector in the same direction as
A, with a magnitude of
. If
c is negative, then the direction of
A is reversed by scalar multiplication.
