Addition of vectors

This function adds two 4-dimensional vectors. To perform the calculation, enter the vectors that are to be calculated and click the Calculate button. Empty fields are counted as 0.

The following formula is calculated

\(\displaystyle\left[\matrix{x1\\y1\\z1\\w1}\right] + \left[\matrix{x2\\y2\\z2\\w2}\right] = \left[\matrix{x1+x2\\y1+y2\\z1+z2\\w1+w2}\right]\)

Description 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 dimensions 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 dimensions.

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.