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1. Hi can some one show me their working for 7)c)ii) please.

Thanks
2. What we want is a line going from A to l and our new line has to be at right angles to l and we want to find the coordinates of this right angle.

So what the question is doing is choosing a suitable point P (which we know has to lie somewhere on l) such that AP is perpendicular with l. It may be easier to show this on a diagram:

http://CoSketch.com/Saved/pzGOONfa

From what we know about the dot product, if two vectors dotted together equal zero then those vectors are perpendicular. So we want to get AP dotted with the direction of l (1, -1, 1) to be zero.

From previous questions we know that that dot product is equal to 7+3p. So we solve 7+3p=0 to give p=-7/3.

So all that's left is to find the coordinates of P. We know that P is on l at the point where lambda=p so the position of P is simply:

(2, -1, 3) + p(1, -1, 1) = (2, -1, 3) - (7/3)(1, -1, 1) = (-1/3, 4/3, 2/3)

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Updated: December 18, 2010
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