Edexcel FP3 - 27th June, 2016

It's in a book called "Further Pure Mathematics" and was written around the time of the Stone Age.

This actual question is from 1976.

https://www.amazon.co.uk/gp/aw/d/0859501035/ref=mp_s_a_1_2?ie=UTF8&qid=1466953157&sr=8-2&pi=SY200_QL40&keywords=further+pure+mathematics&dpPl=1&dpID=51PJ3T067JL&ref=plSrch

Where did you find this???

Thoughts on this one? No idea where to start! I was thinking using the sin A - sin B formula that we never use in C3.

from the question we are told plane 1 has vector equation r.(3,-4,2)=5 and that plane 2 has vector equation r=lambda(2,1,5) + mu(1,-1,-2) -- we can assume from plane 2 that the position vector is (0,0,0) so r=(0,0,0) + lambda(2,15) + mu(1,-1,-2).

Then we want the plane 2 in the form r.n=p.
we then cross multiply (2,1,5) and (1,-1,-2) to give us (3,9,-3)
then r.(3,9,-3)=(0,0,0).(3,9,-3) = 0
r can then be written as r.(1.3,-1)=0 (dividing by 3)

now we have 2 equations r.(1,3,-1)=0 and r.(3,-4,2)=5
which can be written as x+3y-z=0 , 3x-4y+2z=5.
in the mark scheme they had let x=0 which gives us 2 simultaneous equations
3y-z=0, 4y+2z=5
you then solve these for the position vector of the 2 planes
and cross multiply (1,3,-1) and (3,-4,2) for the direction vector.
This may seem complicated due to the amount written but it's fairly simple

Ah I see! Thanks so much for clearing this up!

How do we know that a point on the line exists where x=0?

can someone explain june 2015 8 b) using pythagoras https://3a14597dd5c7aa2363f0675717665774b02557b0.googledrive.com/host/0B1ZiqBksUHNYQWE5bVRTVE9BLW8/June%202015%20QP%20-%20FP3%20Edexcel.pdf

Thoughts on this one? No idea where to start! I was thinking using the sin A - sin B formula that we never use in C3.

at first we don't but later on when we solve the simultaneous equations if we were given a result like 0=0 we would know that the answer is wrong. for these types of question we can always let x,y or z =0 and then proceed to solve simultaneous equations

It must be possible for the line to now be over the origin surely? So will this always work

no problem man

can you explain the reduction question for me pls

could you link me which reduction question?

could you link me which reduction question?

the sinntheta one that you t asked, i just went round and round with cos and sin :'(

from the question it talks about In+2. from this we deduce that we'll need sin((n+2)x)
so I let
sin(nx) = sin((n+2)x-2x)
then i proceeded to just expand that out so sin((n+2)x)cos(2x)-cos((n+2)x)sin(x)
and then yeh just trig from then onwards pretty much

Using that formula got me to the answer so try it

Hm, I actually have no idea what to do. I looked at the final result that we need to show, and figured I'd need to use that formula at some point. But I really have no idea how to progress with it.

Are you able to share a worked solution?