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The book says that RQ and SP are the same. On the drawing I can see that the length is not the same. If two vectors are equal shouldn't the length be equal too?

The book also says that AC is twice the length of both PS Sand QR. How can this be correct? I see that all three vectors are parallel.

The entire task is to express PS, AC, and QR using a b and c.

Translation: The figure shows a square OABC, where P, Q, R, and S is the midpoints on the sides OA, AB, BC and CO. We put OA= a, OB = b, OC = c. Find the vectors PS, AC and QR expressed with a, b, and c. What can we tell about the lines PS, AC and QR?

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    "Firkant" just means it as 4 corners. "Kvadrat" is used for sqaure and "rektangel" for Rectangle.2012-01-12

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Forgetting vectors for a moment and concentrating on line lengths, the question says $P,Q,R,S$ are the respective midpoints of $OA,AB,BC,CO$.

So using similar triangles comparing $OAC$ and $OPS$ and comparing $BAC$ and $BQR$ (as you say, the segments are parallel), it should be easy to see $PS$ and $QR$ are each half the length of $AC$.

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    @Algific: Someone once defined geometry as "the science of drawing correct conclusions from incorrectly drawn figures." Don't be guided by the figure, which is likely to be inexact: be guided by the underlying mathematics.2012-01-03