Difficult A-Level vectors question help!

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djangosheng6969
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I've attempted this question a couple times, but the only information I can seem to extract from the diagrams are that:
vector OM = a +0.5b + 0.5c
vector AS = -a +b +c
I'm not sure how to even go about proving that the two vectors intersect, let alone the exact position vector where they do... any help would be greatly appreciated. The link to the diagram/question is below.

https://i.imgur.com/SGEdBoE.jpg
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CCauston113
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Are you sure this question isn't further maths? I can see how to do it if it is.
(Original post by djangosheng6969)
I've attempted this question a couple times, but the only information I can seem to extract from the diagrams are that:
vector OM = a +0.5b + 0.5c
vector AS = -a +b +c
I'm not sure how to even go about proving that the two vectors intersect, let alone the exact position vector where they do... any help would be greatly appreciated. The link to the diagram/question is below.

https://i.imgur.com/SGEdBoE.jpg
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djangosheng6969
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(Original post by CCauston113)
Are you sure this question isn't further maths? I can see how to do it if it is.
It might be the case that they've made a mistake in setting the practice papers, since I am only doing single maths. However, seeing the further maths solution would be really helpful nonetheless
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CCauston113
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Okay, bear with the fact I'm not on my laptop now so formatting may take a while.
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CCauston113
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Sorry, I realised the method I used didn't work.
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STEM.lover
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Do you know the answer?
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hugebrain
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I think I've got it. Lets start saying D is the point of intersection, what are the vectors OD and AD?
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djangosheng6969
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I don't think I quite follow how you would so soon within the working get to the vector OD, because surely that's already the answer to the question? (position vector of the point of intersection); unless I am missing some key point about the nature of the point of intersection (does it meet halfway across the cuboid or...). Do you have more hints on how to solve it?
(Original post by hugebrain)
I think I've got it. Lets start saying D is the point of intersection, what are the vectors OD and AD?
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Anonymouspsych
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Nope, this is a perfectly doable question using A level Maths knowledge, I just did it...
(Original post by djangosheng6969)
I've attempted this question a couple times, but the only information I can seem to extract from the diagrams are that:
vector OM = a +0.5b + 0.5c
vector AS = -a +b +c
I'm not sure how to even go about proving that the two vectors intersect, let alone the exact position vector where they do... any help would be greatly appreciated. The link to the diagram/question is below.

https://i.imgur.com/SGEdBoE.jpg
(Original post by CCauston113)
Are you sure this question isn't further maths? I can see how to do it if it is.
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Anonymouspsych
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(Original post by djangosheng6969)
I've attempted this question a couple times, but the only information I can seem to extract from the diagrams are that:
vector OM = a +0.5b + 0.5c
vector AS = -a +b +c
I'm not sure how to even go about proving that the two vectors intersect, let alone the exact position vector where they do... any help would be greatly appreciated. The link to the diagram/question is below.

https://i.imgur.com/SGEdBoE.jpg
1) Find vector equation of lines going through OM and AS
2) Set the position vector of both vector equations equal to each other
3) Since a, b & c are perpendicular vectors and hence they are independent vectors so you simply equate the coefficients of a, b & c on both sides of the equation
4) Then you can find the values of the scalar parameters through very simple simultaneous equations.
5) Sub one of the parameters into the corresponding vector equation and voila, you have the position vector of point of intersection
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Gent2324
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(Original post by Anonymouspsych)
1) Find vector equation of lines going through OM and AS
2) Set the position vector of both vector equations equal to each other
3) Since a, b & c are perpendicular vectors and hence they are independent vectors so you simply equate the coefficients of a, b & c on both sides of the equation
4) Then you can find the values of the scalar parameters through very simple simultaneous equations.
5) Sub one of the parameters into the corresponding vector equation and voila, you have the position vector of point of intersection
vector equations of lines are further maths
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Anonymouspsych
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(Original post by Gent2324)
vector equations of lines are further maths
Wait what really?

If so, I apologise lol. I was the last year to do the old spec and we had vector equations in normal A level maths and I didn't think they would've put it in further maths.
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the bear
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(Original post by Gent2324)
vector equations of lines are further maths
they were in the A level syllabus before the recent changes... not any more
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Gent2324
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this question can be done using a little flow chart youre given in further maths, as far as im aware its impossible with normal a level maths knowledge since it specifically mentions lines which you dont really do in normal maths.
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Sir Cumference
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(Original post by Gent2324)
this question can be done using a little flow chart youre given in further maths, as far as im aware its impossible with normal a level maths knowledge since it specifically mentions lines which you dont really do in normal maths.
It’s in an A Level maths new spec practice paper and can be done without FM knowledge. There’s no mention of vector equations of lines in the question.

I’m hoping though that someone else can help because I don’t have time right now to have a go at it!
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Gent2324
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(Original post by Notnek)
It’s in an A Level maths new spec practice paper and can be done without FM knowledge. There’s no mention of vector equations of lines in the question.

I’m hoping though that someone else can help because I don’t have time right now to have a go at it!
what would you do to start with it? i was saying lines because i thought you cant even picture a line in normal maths because theres no way to describe it without a vector or cartesian equation since it goes on infinitely.
come to think of it im guessing it involves the geometry of the cuboid
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nabsers
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I got the point of intersection to be (2/3)a + (1/3)b + (1/3)c. Do you have the mark scheme?
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djangosheng6969
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no, teachers aren't allowed to give us the mark scheme apparently. I got an answer along the same lines, except its more like 1/4c + 3/4 a + 1/4b. That was more on intuition though, and I don't see where 9 marks of working would come from in any case.
(Original post by nabsers)
I got the point of intersection to be (2/3)a + (1/3)b + (1/3)c. Do you have the mark scheme?
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Anonymouspsych
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(Original post by nabsers)
I got the point of intersection to be (2/3)a + (1/3)b + (1/3)c. Do you have the mark scheme?
I got the same answer
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Sir Cumference
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(Original post by Gent2324)
what would you do to start with it? i was saying lines because i thought you cant even picture a line in normal maths because theres no way to describe it without a vector or cartesian equation since it goes on infinitely.
come to think of it im guessing it involves the geometry of the cuboid
Call the point of intersection X and consider the position vector of X in different ways. You should end up with a vector equation that can be solved. I haven’t tried the question so I can’t give more details at the moment.

People who don’t think this is an A Level maths question may need to revise vector geometry problems in their textbook...
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