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How to do a C4 Vectors exam question

Guided solution to an exam question is in the post below this one

C4 Vectors exam questions give a lot of A Level students nightmares, often because they don't fully understand the underlying methods and also because textbooks/teachers don't always prepare students for the kinds of questions that you see in exams. I thought I'd write a solution to an exam question that shows in detail how to draw diagrams and explains all of the methods.

I wrote this solution a few months back but after noticing a lot of vectors queries this year on TSR, I decided today to LaTeX it up and upload it here. Of course an actual solution won't need to be this detailed. If you are a C4 student who hasn't done this question before then I highly recommend trying it yourself before going through my solution.

The question is Edexcel C4 January 2012 Question 7 but it will be useful for all exam boards. Also not all C4 questions are as long as this one, I chose it because it involves a lot of different techniques.

Please let me know if you have any questions or notice any mistakes!
(edited 5 years ago)

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Reply 1



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Alternative method for f) (I highly recommend understanding this):

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(edited 6 years ago)
Thank you so much for this @notnek you have no idea how much I appreciate this! :smile:
Thanks for the tag! I'll definitely have a look at this further once I've finished learning the whole chapter! :smile:
Reply 4
Thanks for this, very helpful :h:


This is hard for Edexcel!? The AQA ones are way worse :cry:
(edited 6 years ago)
Reply 5
Original post by kiiten
Thanks for this, very helpful :h:

This is hard for Edexcel!? The AQA ones are way worse :cry:

Have you looked at the whole question? I'll post the rest of the question now and the solutions over the next few days. The first 3 parts are standard but the 3 parts that are still to come are harder.
Reply 6
Original post by notnek
Have you looked at the whole question? I'll post the rest of the question now and the solutions over the next few days. The first 3 parts are standard but the 3 parts that are still to come are harder.


Oh, no i thought that was one question, my bad :s-smilie:. I didnt know that the rest will make up just one question! :O
Reply 7
Original post by kiiten
Oh, no i thought that was one question, my bad :s-smilie:. I didnt know that the rest will make up just one question! :O

I just posted the rest of the parts above. It's quite a long one!
Reply 8
Original post by notnek
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PRSOM. Looks helpful!
Reply 9
Original post by notnek
I just posted the rest of the parts above. It's quite a long one!


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(edited 6 years ago)
Original post by kiiten

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If the vertices are given as ABCD, then that would normally imply A to B to C to D. But

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Reply 11
Original post by kiiten

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Reply 12
Original post by DFranklin
If the vertices are given as ABCD, then that would normally imply A to B to C to D. But

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Is this wrong?

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(edited 6 years ago)
Reply 13
Original post by kiiten
Is this wrong?

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Reply 14
Original post by notnek

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Reply 15
Original post by kiiten

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Too many spoilers - I'm getting fed up with them :smile:

The vector AB\overrightarrow{AB} is the vector that goes from A to B. In your diagram this vector starts at A and moves up to B.

The vector CD\overrightarrow{CD} is the vector that goes from C to D. In your diagram this vector starts at C and moves down to D.

Since these vectors are parallel but in opposite directions then AB=CD\overrightarrow{AB} =-\overrightarrow{CD}.

EDITED
(edited 6 years ago)
Parts a to c were beautifully explained!! Thanks again for this! I will definitely use this as a reference for when I get stuck on vector questions! I'm excited to read parts d to f now :smile: :smile: :smile:
Reply 17
Original post by notnek
Too many spoilers - I'm getting fed up with them :smile:

The vector AB\overrightarrow{AB} is the vector that goes from A to B. In your diagram this vector starts at A and moves up to B.

The vector CD\overrightarrow{CD} is the vector that goes from C to D. In your diagram this vector starts at C and moves down to B.

Since these vectors are parallel but in opposite directions then AB=CD\overrightarrow{AB} =-\overrightarrow{CD}.


Oh haha i just added them so people who havent seen the answer wont see it :smile:

Do you mean moves down to D?

Oh i thought the arrow determined if the vector is +ve or -ve e.g. if my arrow was pointing to C from D it would be -CD. But youre saying that because CD is going 'downwards' its -CD?
Reply 18
I've updated the second post in this thread with the rest of the solutions. I recommend understanding the alternative method in f) since it may help with harder questions.

If you take anything away from reading my solutions it should be that drawing a clear diagram showing all the information helps a lot with these kinds of questions. Don't be lazy!

Even though I had already written these solutions, formatting them on TSR took a lot longer than I expected. I wonder if I now have the record for most LaTeX in a single post? :smile:

Again, please let me know if you don't understand something or notice a typo/mistake.
(edited 6 years ago)
Reply 19
Original post by kiiten
Oh haha i just added them so people who havent seen the answer wont see it :smile:

Do you mean moves down to D?

Oh i thought the arrow determined if the vector is +ve or -ve e.g. if my arrow was pointing to C from D it would be -CD. But youre saying that because CD is going 'downwards' its -CD?

You're right about my mistake. I meant it moves down to D.

No an arrow on a vector diagram is the vector so if an arrow on your diagram goes from A to B then this arrow represents the vector AB\overrightarrow{AB}

My use of the words "up" and "down" in my last post was just so you can see on your diagram what I was talking about. But a vector going up or down on a diagram doesn't tell you anything about the vector.

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