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单词 DifferenceOfVectors
释义

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

b+d=a.

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.

aba-b..

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

a+(-b)

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.

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更新时间:2025/5/4 17:27:49