Calculator for adding 2-dimensional 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 addition enter the vectors that should be added, then click the 'Calculate' button. Empty elements are counted as 0.
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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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