Multiplication by a Scalar

　　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 3A = 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.