Addition of vectors

Online calculator for adding two vectors with 3 elements

Calculate vector addition

Vectors can be added by adding 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 that should be added and click the Calculate button. Empty elements are counted as 0.


Vector addition calculator

Vector 1Vector 2Result
+ =
Decimal places

Description and formula of the vector addition

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

The following vectors can be added. 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 added.

The following vectors cannot be added 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 added.

The following vectors cannot be added 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 added.

Example

\(\left[\matrix{a\\b\\c}\right] + \left[\matrix{x\\y\\z}\right] = \left[\matrix{a+x\\b+y\\c+z}\right]\)
\(\left[\matrix{1\\2\\3}\right] + \left[\matrix{10\\20\\30}\right] = \left[\matrix{1+10\\2+20\\3+30}\right] =\left[\matrix{11\\22\\33}\right] \)

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


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