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Grade 9/ A Level question help

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Hey guys I was really struggling with this last question of a practice paper and couldn’t understand how to get to the answer. Any help would be very much appreciated!
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ℓove
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It says 'Attachment Not Found'
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zenabdul
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Original post by ℓove
It says 'Attachment Not Found'


I’m sure it doesn’t, I’ll try to post it again anyway
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zenabdul
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26330F65-BAD7-4F3B-96CF-7FF06D2B8DA2.jpg.jpeg
Original post by zenabdul
I’m sure it doesn’t, I’ll try to post it again anyway


Well it did when I tried to look at it. However your latest post shows it.

So, MPN is a straight line.

This means MP will be a multple of PN (parallel vectors), or of a multiple of MN (either one).

I.e. MP = mPN for some unknown scalar m.

If we can express each of those in terms of a,b,

For them to be equal they must have the same scalar for the vector a on each side, and the same scalar for the vector b on each side (not necessarily the same as a's), since a,b are not parallel.

You now have two equations in two unknowns, k,m. And solve.
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zenabdul
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Original post by ghostwalker
Well it did when I tried to look at it. However your latest post shows it.

So, MPN is a straight line.

This means MP will be a multple of PN (parallel vectors), or of a multiple of MN (either one).

I.e. MP = mPN for some unknown scalar m.

If we can express each of those in terms of a,b,

For them to be equal they must have the same scalar for the vector a on each side, and the same scalar for the vector b on each side (not necessarily the same as a's), since a,b are not parallel.

You now have two equations in two unknowns, k,m. And solve.


Thanks, so I shouldn’t use AP and kAB
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zenabdul
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Original post by ghostwalker
Well it did when I tried to look at it. However your latest post shows it.

So, MPN is a straight line.

This means MP will be a multple of PN (parallel vectors), or of a multiple of MN (either one).

I.e. MP = mPN for some unknown scalar m.

If we can express each of those in terms of a,b,

For them to be equal they must have the same scalar for the vector a on each side, and the same scalar for the vector b on each side (not necessarily the same as a's), since a,b are not parallel.

You now have two equations in two unknowns, k,m. And solve.


I don’t you can express PN in terms of a and b
Original post by zenabdul
Thanks, so I shouldn’t use AP and kAB


I didn't give all the details in my response, assuming you're familiar with the basics.

You will need AP and kAB.

Original post by zenabdul
I don’t you can express PN in terms of a and b


You can. Find N, find P and hence PN.
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Original post by ghostwalker
You can. Find N, find P and hence PN.


Do you mind showing me how to get to the answer
Original post by zenabdul
Do you mind showing me how to get to the answer


In spoiler.

But, I'd rather you'd had a go yourself and posted some working.


Spoiler

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zenabdul
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Original post by ghostwalker
In spoiler.

But, I'd rather you'd had a go yourself and posted some working.


Spoiler



Thanks , I understand how to answer it, I’ve checked it as well
Original post by ghostwalker
In spoiler.

But, I'd rather you'd had a go yourself and posted some working.


Spoiler





How do you eliminate m if m is not in both sides of the equation?
Original post by ghostwalker

Spoiler





I don't understand what you have done here, rest I get. Thank you
Edit: Think I got it.

Spoiler

(edited 5 years ago)
Original post by clock087
...


The equation can be rearrange to get all the "a"s on one side and all the "b"s on the other. And they are equal.

a and b are two non-parallel vectors. As such the only way a multiple of a can equal a multiple of b, is if that multiple is zero in each case.

Going back to the first equation, this is the same condition as the multiple of a on the left must equal the multiple of a on the right. Similarly for the b's.
(edited 5 years ago)
Original post by clock087
I don't understand what you have done here, rest I get. Thank you
Edit: Think I got it.

Spoiler




In case it helps: http://burymathstutor.co.uk/EdexcelGCSEMathsNovember2017Paper3vectorQ.pdf

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