Maths P2 ECZ/GCE VECTORS - 2026 Preps

追加: 2026-05-11

[00:00:00]Hello. Greetings. This is a wonderful question on the board that I want us to answer together. This is falling under vectors. So, this is mathematics and I just want you to understand these questions. So, follow me clearly and attentively. I want your total attention.

[00:00:26]In the diagram below, ABC So, ABC and AD are straight lines. This is a straight line and that one is a straight line. CD CD and BE intersect at F so that this ratio given can be true. Have you seen this that has been given? We are told to say that BF is one. BF So, this part that is here, that is a one. So, this one is a one. So, that is one. Then, we are told FE is two.

[00:01:12]FE This is two. So, we put a two there.

[00:01:16]This is what we need to get. So, this one which corresponding value is that other one. So, this one that is here is this one. Then, this one is that one.

[00:01:29]That is what is given.

[00:01:33]B is the midpoint of AC. B is the midpoint of AC and D is the midpoint of AE. This is the information that has been given. Given that AB is equal to vector Q. AB is equal to vector Q. So, meaning this this is the midpoint of AC.

[00:01:53]Meaning that even from here to there, this is also what? Q. Have you seen? And this is the midpoint. Even from here up to there, this is also P. So, meaning that this all line, to make you understand, this all line AE is two P. Have you seen? Then AC is two Q, the whole line. Since this is the midpoint, so this one and that one, have you seen?

[00:02:20]This is the midpoint of these two. So, this is it.

[00:02:24]So, express as simply as possible in terms of P [clears throat] and or Q.

[00:02:32]So, vector P and or vector Q. First question, BE. So, first question, this is BE. How do we answer this one?

[00:02:44]So, this is simple. Vectors, we move in a triangle way like this. Pa. Pa. So, if you are told to say, uh find the the if this is A BC. So, if we are told to find vector AC, we move AB BC. Have you seen? We move like this. Pa. You just remove. Pa.

[00:03:07]Pa.

[00:03:08]This is how we get to move. Two steps.

[00:03:10]One, two. So, we are told to find BE. We are told to find BE. How are we going to move? BA. So, we are going to say BA plus AE. So, that is vector BA. BA plus [clears throat] AE. AE. AE. Have you seen? Plus AE. AE. Plus AE. AE. This is what we need to get. So, this is now equal to what? What is BA?

[00:03:44]BA. We are now going against since the vector is going this side. We are going against. So, it is negative what? Q.

[00:03:54]Vector Q.

[00:03:55]Then we say plus C. What is AE? What is AE? AE. This all thing, P plus P is 2P.

[00:04:06]So, [clears throat] plus what? 2P. So, plus vector 2P. So, meaning that that is our answer. That's how you are supposed to answer it.

[00:04:18]We move to this one.

[00:04:20]FE FE So, FE, where is F?

[00:04:27]F is here, E is there. How are we going to move? You can't move like pa pa. You see you are you've run out of your steps. We just move We just needs to move in two steps. But, if you look at this one, FE is along this line. Have you seen? What is the name of this line?

[00:04:49]BE. So, no need of moving.

[00:04:52]It is along this particular line. So, FE FE is along BE. E. So, this is equal FE.

[00:05:03]There is this capacity which is two. The total line BE is 1 plus 2 3. So, it is 2 over 3. Then it is along which line? BE like this.

[00:05:18]This is what you need to do. Then BE we've solved. This is the one on top there. So, meaning that the answer finally is equal to 2 over 3. Then we've got negative Q plus 2P like this. So, if you want, you can end there. There's no problem. That is your answer. If you want, you can simplify, but you can end there. So, that is the what? That is our answer. That is the answer that we get.

[00:05:47]Just one mark, one mark, one mark. We go to C.

[00:05:52]This one that is here, C. How do we answer C? For us to answer C, I guess this is visible. We are able to see everything that is there. So, how do we answer C? D F.

[00:06:06]So, D F. How are we going to answer D F?

[00:06:10]Uh D, where's D? D F. From here to there. Have you seen? Here to there. Do we know D C? We don't know. So, this is the reason why I can't say that, "Okay, we just get this cap up to the all line we know it." Here we don't know it. So, we'll go with the step way. So, this is D F. We are going to say D E then F E.

[00:06:32]Have you seen? This is how we are going to say. D E. So, D E like this vector D E plus E F plus E. Have you seen then F like this? This is what I'm going to do.

[00:06:47]Therefore, the answer is what? D E D E.

[00:06:50]This is P. So, I say P then plus C. Have you seen plus? What is E F? What is E F?

[00:06:59]E F now, what I'm going to do now? Since there is I'm going against this is F E.

[00:07:07]This is E F against now. I'm starting from here going this side. So, meaning that instead of putting a plus here, I'm going to say minus C because I'm going against minus 2 over 3 then I do this negative Q plus 2 P like this.

[00:07:26]Then now you can see P here and there is P there. So, I can further work out this.

[00:07:32]How can I work out that? So, meaning that I've got something like this. Want you to get this. There is P there minus So, if I multiply negative negative, that is positive here. This going to be positive. Then two Q over three. Have you seen? Then negative times positive, that is negative. Then I'm going to have two times two, that is four. So, four P over what? Three. The denominator will fall. These two are like terms. So, P minus four P over three. Then plus two Q over three. I work out this particular part, this one that is here. So, I work out this common denominator three.

[00:08:20]Like this. One into three, it is three.

[00:08:22]Three times P, that is three P minus three into three one. Have you seen?

[00:08:30]Then one times four P. That is four P. So, this is now equal to negative P over three. Have you seen? Then plus two Q over three. So, this can be written as one over three like this. Then I can start with this one that is here. Two Q then minus P. I can write it like this if I want. So, this and that, it is just one and the same. But I know if I write like this, some people will be confused.

[00:09:06]So, it's better I teach this in an easy way. And as we get to improve, as we get to go deeper than this, we are going to be improving. So, what I'm going to say here D F is equal to So, now what I need to do, I'm going to start with this one that is a positive.

[00:09:26]So, that is two Q over what? Three.

[00:09:32]Then minus, there is a minus, minus P over three.

[00:09:38]So, this is the answer. That is the answer. That's how you are supposed to do it. I taught you that this can also be we can write this in 1/3 open bracket, but I don't want to go that way because I know there are people that are trying to get this. There are people that are pushing so hard so that they understand.

[00:09:59]So, if I go that way, I may end up making them feel as if this topic is so difficult, but this is one of those simplest topics. One one one mark. This is getting one mark each. So, given also that DC is equal to this, write down an expression for DC. First part, DC. So, DC is equal to what? DC is equal to H D F like this. Where I say, "Okay, then DC, just an expression." H, then DF is this one. Are you seeing? DF is this. This is DF. Are you seeing? So, I just say open bracket, then I say 2Q like this, over three. Are you seeing? Minus P over three like that. Then, I can multiply this. So, this can we can I can write this as this can also be DC is equal to H times everything here. That is 2H over three and the Q there.

[00:11:10]Minus, I'm going to have what? I'm going to have H over three and the P there.

[00:11:17]So, that is an expression.

[00:11:20]No need of calculating anything there.

[00:11:22]That is just an expression. So, this is an expression. And hence, show that HC.

[00:11:30]Now, we are told to show that. So that party, what I need to do I'm told to show that AC. So I'm told to find AC I mean. AC is equal to what? I want to find AC. AC, how should I move? AC, I need to say what? So how should I move? AD AD vector AD plus DC plus DC like this. Which is now equal to AD.

[00:12:07]AD, that is P. I put my P there. Then I say plus. What is DC? DC, where is DC?

[00:12:17]Where is DC? DC is this part that is here. Have you seen? This is a part that is here.

[00:12:24]I want you to get this. I want you to get this. Have you seen this part that is here? If I want I can start with this negative. So this is I can start with this one where I say instead of writing plus here I say minus H over 3 P. Then this is plus 2 H over 3 then a Q there.

[00:12:48]Have you seen? So that I factorize this part that is here. Instead of rewriting the same thing, I can start with this.

[00:12:57]At first, if you remember very well, it was like this. Then I said that we can start with a positive. You need to know how to change numbers. When I say 3 minus 2, this is just the same as negative 2 plus 3. These two are just the same. This one and this one, they are just the same. So just swapped them.

[00:13:22]So you need to know how to swap. When you are swapping, nothing is crossing an equal sign. So, the signs are maintaining. I factorize this part that is here. So, SC is equal to what? What letter is common there? This is what? P.

[00:13:40]They've written the P outside. They do this. I do that. Then the P outside there.

[00:13:46]Then P into P, that is what? Minus. Then here I'm going to remain with H over three. The P will cancel out to the P.

[00:13:57]Then I say plus. Plus what? Two H over three and A cubed. Have you seen this one? Hence proven. You just say hence see. They want you to show. Hence see.

[00:14:09]Shown.

[00:14:11]It's just as simple as that.

[00:14:13]I don't know if you were getting that, but that is how it is supposed to be.

[00:14:19]The same way I've answered it like that, that is how you need to do it. And that's how it must be answered. So, this is it. This is the question that I had for you. If you're looking for more questions, we are going to answer together such questions. Don't forget to like the video. Don't forget to share it. Don't forget to even subscribe to this particular channel or page. This is your full-time online tutor, Harrison J.

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