Vector Scalar Multiplication

The calculator on this page multiplies a vector of 2, 3 or 4 elements by a real number.

To calculate, select the number of elements (3 is the default). Enter the values and click on the 'Calculate' button.

The value 0 is assumed for empty fields.

Description and formula

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 points in the same direction as the original one. If the scalar is negative, it points in the opposite direction in the opposite direction.

Vector and scalar are multiplied by multiplying the individual elements of the vector by the scalar.

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

Example

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