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Vectors

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Hi, I can do all of the question except the 1 marker at the end (the geometrical interpretation one). The markscheme says the answer is 'Either: E lies on AB and is such that AE : EB = 1 : 2. Or: E is the point of intersection of AB and CD'. I don't understand it at all, thanks in advance!
Original post by rpnom
vector.png



Hi, I can do all of the question except the 1 marker at the end (the geometrical interpretation one). The markscheme says the answer is 'Either: E lies on AB and is such that AE : EB = 1 : 2. Or: E is the point of intersection of AB and CD'. I don't understand it at all, thanks in advance!


e = 2/3a + 1/3b = a + 1/3(b - a), i.e. vector A + 1/3*vector AB. Thus E is 1/3 of the way along AB, so it divides AB in the ratio 1:2.

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