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 1Vector 2Result
- =
Decimal places

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.


Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?