A vector equation can be multiplied with a scalar equation by multiplying every component of equation with equation.

    equation

By multiplying with a scalar, the magnitude of the vector changes (unless the scalar is one). For example, multiplying a vector by 2 will make it twice as long. Multiplying with a negative number will reverse the orientation. If the scalar is -1, the orientation will stay the same but the vector’s head and tail are reversed.

Example

We multiply the vector equation by a scalar:

(1)   equation