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# Vectors and geometry watch

1. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a
and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD,
(iii) BD and (iv) AC.
2. Assuming my understanding of the question is correct, think about what a+b and a-b look like.
3. a-b will be a vector parallel to the vector DB while the vector a+b will be a vector from the point A through the point C to a point say E to form a parallelogram APEQ. I don't get what to do from there. However, thank you for your reply.
4. Still assuming that I understood the question - perhaps you could post your diagram to confirm?
(Original post by cathedra x)
a-b will be a vector parallel to the vector DB while the vector a+b will be a vector from the point A through the point C to a point say E to form a parallelogram APEQ.
From my understanding of the question, we agree. Specifically, think about the lengths of a-b and a+b. You should be able to multiply by suitable constants to get BD and AC. AB and AD can then be derived from those.

Another approach would be to write vector equations and solve those, e.g.
a = AB + BC/2 (I won't write the other one), and noting that AB = DC etc.
5. (Original post by cathedra x)
ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a
and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD,
(iii) BD and (iv) AC.
it is best to write vectors in bold; in the exam do a squiggle underneath ?
6. This is my diagram.
7. OK, I had two equations
a=AB+BC/2
but AD=BC and DC=AB, so eqn 2 becomes
b=BC+AB/2
Solving these 2 equations simultaneously, I had AB and DC, and found the other vectors from there.
So thank you guys for your help. I appreciate your help very much.

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