Math CentralQuandaries & Queries


Question from Nazrul, a teacher:

If a, b, c be three vectors how can I prove that
(i) -(a+b)=-a-b
(ii) If a+b =c then a= c-b
Thank you.

Hi Nazrul,

The easiest way to prove these equivalent statements about vectors is geometrically, I'll just show the first one:

Remember that vector -a means that it has the same magnitude (length) as vector a but an opposite direction. If you draw any vectors a & b their resultant vector is a+b. If you draw vectors -a &-b their resultant vector is -a+(-b)=-a-b. If you draw -(a+b), it coincides with -a-b.

Hope this helps,



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