# Multiply a vector by a scalar

Online calculator for multiplying a vector with 3 elements and a number

## Calculate vector-scalar multiplication

This function multiplies a vector by a real number.

To perform the multiplication, enter the vector and real number to be multiplied and click the Calculate button. Empty fields are counted as 0.

Vector scalar multiplication calculator

 Vector Scalar Result * = Decimal places 0 1 2 3 4 6 8 10

## Description of the vector-scalar multiplication

Vectors can be multiplied by real numbers. The real number is called a scalar to distinguish it from vectors.

If the scalar is positive, the resulting vector will point in the same direction as the original. If the scalar is negative, it points in the opposite direction.

Vector and scalar are multiplied by multiplying the individual elements of the vector with the scalar. Is calculated:

$$\displaystyle\left[\matrix{a\\b\\c}\right] \cdot x = \left[\matrix{a \cdot x\\b \cdot x\\c \cdot x}\right]$$

### Example

$$\displaystyle\left[\matrix{2\\3\\4}\right] \cdot 5 = \left[\matrix{2 \cdot 5\\3 \cdot 5\\4 \cdot 5}\right] = \left[\matrix{10\\15\\20}\right]$$