Vector Subtraction
Online calculator for subtracting vectors
The calculator on this page subtracts vectors with 2, 3 or 4 elements.
To calculate, select the number of elements (3 is the default). Enter the values of the two vectors and click on the 'Calculate' button.
The value 0 is assumed for empty fields.
|
Formulas and examples for vector subtraction
The following article describes vector subtractions using vectors of two or three elements. Basically, vectors can contain any number of elements.
Vectors can be subtracted by adding the individual elements. However, vectors can only be subtracted if they have the same number of dimensions and the same orientation (columns or row-oriented).
The following vectors can be subtracted. They have the same number of elements and same orientation.
\(\left[\matrix{X_a\\Y_a}\right] - \left[\matrix{X_b\\Y_b}\right]\) and \(\left[\matrix{X_a\\Y_a\\Z_a}\right] - \left[\matrix{X_b\\Y_b\\Z_b}\right]\)
The following vectors can not be subtracted because they have a different number of elements.
\(\left[\matrix{X_a\\Y_a}\right] - \left[\matrix{X_b\\Y_b\\Z_b}\right]\)
The following vectors can not be subtracted because they have a different orientation.
Example
\(\left[\matrix{a\\b}\right] - \left[\matrix{c\\d}\right] = \left[\matrix{a-c\\b-d}\right]\)
\(\left[\matrix{3\\5}\right] - \left[\matrix{1\\4}\right] = \left[\matrix{3-1\\5-4}\right]=\left[\matrix{2\\1}\right] \)
The subtraction on vectors of higher dimension is according to the same principle.
\(\left[\matrix{a\\b\\c}\right] - \left[\matrix{x\\y\\z}\right] = \left[\matrix{a-x\\b-y\\c-z}\right]\)
\(\left[\matrix{10\\20\\30}\right] - \left[\matrix{1\\2\\3}\right] = \left[\matrix{10-1\\20-2\\30-3}\right] =\left[\matrix{9\\18\\27}\right] \)
Graphic Vector Subtraction
The following figure shows the graphic vector subtraction of the expression
\(\left[\matrix{5\\5}\right] - \left[\matrix{4\\2}\right] = \left[\matrix{5-4\\5-2}\right]=\left[\matrix{1\\3}\right] \)
First the line of the first vector (red) is drawn from the zero point to the position \(x = 5, y = 5\).
Then, from the top of the first vector, the second vector (yellow) is drawn to the position by 4 units to the left and 2 units to the bottom.
The sum vector (blue) is determined by the line from the base point of the first to the peak of the second vector
The addition of vectors is identical to the subtraction of vectors, but with positive operator. The same rules apply to the vector addition as to the vector subtraction.
Vector Functions
Addition • Subtraction • Multiplication • Scalar Multiplication • Division • Scalar Division • Dot Product • Cross Product • Interpolation • Distance • Distance Squaret • Normalization • Reflection • Magnitude • Squared-Magnitude • Triple-Product
|
|