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The diagonals of a plane quadrilateral ABCD intersect at O, and X,Y are the mid points of the diagonals AC and BD respectively. Show that: (vectors) (i) 2AB + 2BC + 2CA = O and (ii) If OA + OB + OC + OD = 4OM, find the location of M

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Now (i) doesn't look right to me as O is not a vector? Any one shed any light on this
1) I think it is not O but 0 (zero) ABC form a triangle hence AC = AB + BC (vector addition). Hence AB +BC+CA = 0
yes i think you're right, its def a typo in the book

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Other answers:

the last part turns out to be mid XY not sure how to prove that? I'll post the question again...

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