Vector Proofs

[Stroodle]

Anyone know if there are likely to be involved vector proofs on the exam? (haven't done the past ones yet). It's the only area I'm really struggling with at the moment..

[Martoman]

I look at it logically. If they do they have to guide you through it and most DEFINATELY give you a picture defining all the variables because from the markers point of view it would be a NIGHTMARE going through each persons working because it doesn't correspond to their answer sheet next to them. So i'd expect not so much a proof but just questions on the properties of vectors in the context of stuff you've done on proof ie:

A right angled trianlge ABC the hypotenuse is AC = -4i +j. If BC is parallel to vector -3i+2j, find AB.

[jasonn93]

A right angled trianlge ABC the hypotenuse is AC = -4i +j. If BC is parallel to vector -3i+2j, find AB.

Heff '09 ?

[Martoman]

exactly, i liked it. There solutions was retarded though. So much quicker to just do it as a.a = b.b + c.c (a generalised case of a right angled triangle ABC) that is.

[theuncle]

@martoman
how does that work if you don't know the magnitude of BC?

[Martoman]

ac.ac = 17

BC = -3mi+2mj parallel to that by some multiple m

AB = AC + CB = (3m-4)i+(1-2m)j

Ac.Ac=Ab.Ab + Bc.Bc

17 = (3m-4)^2+(1-2m)^2+9m^2+4m^2

17 -17 = 26m^2-28m

m = 14/13

Sub in m into AB to get Ab I hope thats all right as i can't find a pen atm

[theuncle]

Ah ok cool.
I used the dot product of perp vectors=0.
Pretty sweet how two different methods give the same answer

[Martoman]

Ah ok cool.
I used the dot product of perp vectors=0.
Pretty sweet how two different methods give the same answer

To quote Tom Lehrer, my idol, "thats mathematics!!!"

[kamil9876]

yep. very sweet indeed. When noticing something like this you can find some nice identities, I remember finding multiple solutions to problems leading to proofs of various theorems.

e.g: prove the double angle formula sin(2x)=2sin(x)cos(x) by figuring out the area of an isosceles triangle with side lengths 1 (angle 2x in between them) in two different ways. extension: extend this method to proving sin(x+y)=...