# Subtraction of vectors

Online calculator for subtracting two vectors with 3 elements

## Calculate vector subtraction

Vectors can be subtracted by subtracting the individual elements. The following formula is calculated.

$$\displaystyle\left[\matrix{x1\\y1\\z1}\right] - \left[\matrix{x2\\y2\\z2}\right] = \left[\matrix{x1-x2\\y1-y2\\z1-z2}\right]$$

Enter the vectors to be subtracted and click the Calculate button. Empty elements are counted as 0.

Vector subtraction calculator

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

## Description of vector subtraction

Vectors can be subtracted by subtracting the individual elements. However, vectors can only be subtracted if the number of dimensions and their direction (column or row-oriented) are the same.

The following vectors can be subtracted. They have the same number of elements and direction.

The vectors $$\left[\matrix{X_a\\Y_a}\right] - \left[\matrix{X_b\\Y_b}\right]$$     and    $$\left[\matrix{X_a\\Y_a\\Z_a}\right] - \left[\matrix{X_b\\Y_b\\Z_b}\right]$$ can be subtracted.

The following vectors cannot be subtracted because they have different numbers of elements.

The vectors $$\left[\matrix{X_a\\Y_a}\right] - \left[\matrix{X_b\\Y_b\\Z_b}\right]$$ cannot be subtracted.

The following vectors cannot be subtracted because they have a different orientation.

The vectors    $$[X_a\;Y_a\;Z_a]- \left[\matrix{X_b\\Y_b\\Z_b}\right]$$ cannot be subtracted.

Example

$$\left[\matrix{a\\b\\c}\right] - \left[\matrix{x\\y\\z}\right] = \left[\matrix{a-x\\b-y\\c-z}\right]$$
$$\left[\matrix{10\\20\\30}\right] - \left[\matrix{1\\2\\3}\right] = \left[\matrix{10-1\\20-2\\30-3}\right] =\left[\matrix{9\\18\\27}\right]$$

Further information on vector subtraction can be found in the RedCrab tutorial.