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Vectors. Grrr. watch

1. Edexcel C4 textbook, excercise 5k question 2. >_>;

The position vectors of the points A and B are relative to an origin O are 5i+4j+k, -i+j-2k respectively. Find the position vector of the point P which lies on AB produced such that AP=2BP.

I thought of drawing a diagram, so:

This means that:

Now what?
2. (Original post by wanderlust.xx)
Edexcel C4 textbook, excercise 5k question 2. >_>;

The position vectors of the points A and B are relative to an origin O are 5i+4j+k, -i+j-2k respectively. Find the position vector of the point P which lies on AB produced such that AP=2BP.

I thought of drawing a diagram, so:

This means that:

Now what?
You also have the equation AP + PB = AB, and you can solve that simultaneously with the other equation you got, I think.

EDIT:

Forget that.

You know the vector OA and you can work out the vector AB (It's the same as OB - OA) and then you can just plug those right into the equation that you got

Actually, I think there are two answers.

Your first equation could also be: OP = a + 2(AB)
3. (Original post by tazarooni89)
You also have the equation AP + PB = AB, and you can solve that simultaneously with the other equation you got, I think.

EDIT:

Forget that.

You know the vector OA and you can work out the vector AB (It's the same as OB - OA) and then you can just plug those right into the equation that you got

Actually, I think there are two answers.

Your first equation could also be: OP = a + 2(AB)
P is on AB produced and so the order of the letters will be A, B, P. It follows that B is the midpoint of AP. Hence vector AB = vector BP. Etc.
4. Maths Buster actually right. First you've to find out AB = b-a

Then use the condition AP = 2BP. i.e. AP = 2AB.

Therefore you can find out OP.

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