Subtraction of vectors

The following formula is calculated

\(\displaystyle\left[\matrix{x1\\y1}\right] - \left[\matrix{x2\\y2}\right] = \left[\matrix{x1-x2\\y1-y2}\right]\)

To perform the subtraction enter the vectors, then click the 'Calculate' button. Empty elements are counted as 0.

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.