Can I do this? (vectors) (1 Viewer)

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(the red arrow) In vectors are you allowed to just factorise out something when it equals to zero like in algebra, because the solution expands it and then equates them, so is my way wrong?
 

yourlocaliga

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im inclined to say no bc i think my teacher said somethign about not being allowed to do that but im not 100% sure
 

C2H6O

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im not sure whether null factor applies to dot product, but idk if youre able to treat dot product as multiply in this case? like wouldn't it be (c-a).(1/2c+a)?
 

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