Online calculator for adding two vectors with 2 elements
The following formula is calculated
\(\displaystyle\left[\matrix{x1\\y1}\right] + \left[\matrix{x2\\y2}\right] = \left[\matrix{x1+x2\\y1+y2}\right]\)

Addition 
Subtraction 
Multiplication 
Scalar Multiplication 
Division 
ScalarDivision 
Scalar Product 
Interpolation 
Distance 
Distance Square 
Normalization 
Length 
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 roworiented) 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.
