difference of vectors

Let a and b be two vectors in the plane (or in a vector spaceMathworldPlanetmath).  The difference vector or differencea-b  of a and b is a vector d  such that


Thus we have

b+(a-b)=a. (1)

According to the procedure of forming the sum of vectors by setting the addends one after the other, the equation (1) tallies with the picture below; when the minuend and the subtrahend emanate from a common initial point, their difference vector can be directed from the terminal point of the subtrahend to the terminal point of the minuend.


Remark.  It is easily seen that the difference a-b is same as the sum vector


where -b is the opposite vector of b:  it may be represented by the directed line segment from the terminal point of b to the initial point of b.

Title difference of vectors
Canonical name DifferenceOfVectors
Date of creation 2013-03-22 17:47:19
Last modified on 2013-03-22 17:47:19
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Definition
Classification msc 53A45
Synonym vector difference
Synonym vector subtraction
Related topic CommonPointOfTriangleMedians
Related topic Difference2
Related topic ProvingThalesTheoremWithVectors
Related topic VectorValuedFunction2
Defines difference vector
Defines opposite vector