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School of Mathematics and Statistics, The University of Sydney
 3. Addition and subtraction of vectors
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Subtraction of vectors

Page 5 of 7 

Subtraction of two vectors is just a special case of addition. The vector u - v is defined to be

u - v = u + (-v).

Using the parallelogram law of addition, u - v = u + (-v) = ---> OA + ---> OC = ---> OQ.

v A O u u - v - v Q C

The vector v - u can be found in the same way.

----> ----> ---> v - u = v + (-u) = OB + OD = OR.

B R v-u v O u D-u

The vectors u + v and u - v are both diagonals of the parallelogram formed by u and v.

u + v v u - v u

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