Vectors year 13

https://imgur.com/a/fvc9Ygj

Could someone help me with this question? I get that I need to find fp and then pe and show that they are scalars of each other but I’m stuck on finding fp? Because I’m doing fp is fc, co, OA, and then ap but I can’t work ap out. In the solution bank they have ap as 4/3 am and I’m confused as to how they got that. Any help would be greatly appreciated! :smile:

Reply 1

mqb2766

Original post

by username79352

https://imgur.com/a/fvc9Ygj
Could someone help me with this question? I get that I need to find fp and then pe and show that they are scalars of each other but I’m stuck on finding fp? Because I’m doing fp is fc, co, OA, and then ap but I can’t work ap out. In the solution bank they have ap as 4/3 am and I’m confused as to how they got that. Any help would be greatly appreciated! :smile:

Have you done the first part so show that P lies on EF?

But AM:MP = 3:1 so AM is 3/4 of AP ....

If youve done the first part, a simple (but not what they want - vectors) argument would be to say triangles PEM and OAM are similar with a side ratio of 1:3 (given) so FP (OA) : PE = 3:1 and hence the desired ratio is 2:1.

Reply 2

Nitrotoluene

Original post

by username79352

https://imgur.com/a/fvc9Ygj
Could someone help me with this question? I get that I need to find fp and then pe and show that they are scalars of each other but I’m stuck on finding fp? Because I’m doing fp is fc, co, OA, and then ap but I can’t work ap out. In the solution bank they have ap as 4/3 am and I’m confused as to how they got that. Any help would be greatly appreciated! :smile:

Suppose that your home is at the point O. The vectors a, b, and c denotes the steps that need to be taken for the movement from your home to the spots A, B, and C. Based on the locations of points E, M, and P, the method of traveling from the vector OE to home (O) and then to the point E (vector OE) can be done with a, b, and c vectors. We can say that M lies on line OE and divides it in the ratio 3:1 indicating its position very clearly. It is possible to find M and P - if such that AM:MP is 3:1 - by using the vectors from (A, M, P) to A, M, and P. The direction of vectors EP and EF will determine if point P is on line EF. As an additional statement, vector EP in conjunction with point F will provide EF. You can get the position of point P by checking the slopes. Otherwise, feel free to ask me.
Here is my 2 cents!

Reply 3

username79352

Original post

by mqb2766

Have you done the first part so show that P lies on EF?
But AM:MP = 3:1 so AM is 3/4 of AP ....
If youve done the first part, a simple (but not what they want - vectors) argument would be to say triangles PEM and OAM are similar with a side ratio of 1:3 (given) so FP (OA) : PE = 3:1 and hence the desired ratio is 2:1.

Could I just make two similar triangles and then say that as fe is a and by using my triangle show pe as one third of a and so fp. Is two thirds and as they are parallel p lies on fe. Would that be allowed for showing p lies on EF? And then just do the ratios or would I lose marks for for that?

Reply 4

mqb2766

Original post

by username79352

Its obviously a vector question, so you should make sure you understand the model solution.

To argue that p lies on EF, the angles at P are the same and the enclosing sides have the same ratio (given) so PE is parallel to OA as is EF, so P must lie on EF.

As long as the question didnt specify a method and you properly justified it, you should get full marks. However, if youve not practiced it, Id use it as a fall back method so use it if you cant get the "proper"/vector way to work.

(edited 11 months ago)

Reply 5

username79352

Ok thanks, I managed to do both ways it was just the fact that ap was 4/3 of am that confused me but then I realised what they did.

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