Question 417490
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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