# Alevel further maths - vectors

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Thread starter 4 weeks ago
#1
Would anyone be able to show me their working for this question from the edexcel website? There is no mark scheme and I don’t know what to do.
Last edited by Latte Lamila; 4 weeks ago
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4 weeks ago
#2
What have you done so far?
I suggest you start by drawing a diagram and get an idea of what the shape APQC looks like and how it relates to the various vectors described.
Last edited by DFranklin; 4 weeks ago
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Thread starter 4 weeks ago
#3
I worked out P to be (4.75, 2.75, 5) and Q (7,3,-2) . I think I’ve gone wrong somewhere because I still can’t figure out the shape of APQC. And for the area of the quadrilateral is it just the cross product?
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4 weeks ago
#4
Have you drawn a diagram as I suggested? Can you post it?
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Thread starter 4 weeks ago
#5
(Original post by DFranklin)
Have you drawn a diagram as I suggested? Can you post it?
My diagram is really terrible, all 4 sides of my quadrilateral would be different lengths according to my P and Q. I assume it’s meant to be a parallelogram since I know how to calculate the area of that. I’ll attach my working for P and Q too because that’s probably the issue. I apologise if the image turns out sideways I don’t know how to fix that.
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4 weeks ago
#6
The points mentioned in the question are A, B, C, P and Q (and the plane π).

Without doing any calculations, but using the information given about how these things relate (e.g. that P is where the line AB intersects π), draw a diagram showing all the points, the relevant lines, and the plane π (you can represent π as a simple line intersecting both AB and BC).

Once you do that, you should be able to see how to represent the quadrilateral as "a shape you know how to find the area of" minus "another shape you know how to find the area of".

Note that two opposite sides of the quadrilateral are parts of the lines AB, BC, so it isn't a parallelogram.
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Thread starter 3 weeks ago
#7
Thanks so much for the explanation, when I redrew the diagram I was able to get the answer! For part b, would k be 2 and 8.6 and am I missing any other values? I used the scalar triple product.
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3 weeks ago
#8
(Original post by Latte Lamila)
Thanks so much for the explanation, when I redrew the diagram I was able to get the answer! For part b, would k be 2 and 8.6 and am I missing any other values? I used the scalar triple product.
The approach sounds right. I haven't actually done any calculations, so I couldn't tell you if your values are right. (it's the method that matters, anyhow).
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