SOLUTION: Three vectors a,b and c are such that a.(b+c)=b.(a+c) Show that c must be perpendicular to a-b.

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Question 417490: Three vectors a,b and c are such that a.(b+c)=b.(a+c)
Show that c must be perpendicular to a-b.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We only need to show that c.(a-b) = 0 or (a-b).c = 0



a.(b+c)=b.(a+c)

a.b+a.c = b.a + b.c

a.b+a.c = a.b + b.c

a.b+a.c-a.b = a.b + b.c - a.b

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

0+a.c = 0 + b.c

a.c = b.c

a.c - b.c = 0

(a-b).c = 0


Therefore, c is perpendicular to a-b


Note: you can draw a picture to accompany the proof, but don't rely exclusively on it (as it may not be drawn correctly)


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