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A2 Maths Vectors

Hi everyone,

I'm having real trouble figuring out how to do part ii).


The track for an overhead railway lies along DEF, where D and E have position vectors d = 130i - 40j + 20k and e = 90i - 20j + 15k, and F is a point on the ski-slope.

i) Find the equation of the straight line DE.

This equals r = (130i - 40j + 20k) + λ(8i - 4j + k), as far I can see.
But then part ii)...

ii) Find the position vector of the point F.

I'm at a loss, any help is much appreciated!
F is a general point on slope so if you had to express it algebraically, how would you?
Reply 2
Original post by Geometrica
Hi everyone,

I'm having real trouble figuring out how to do part ii).


The track for an overhead railway lies along DEF, where D and E have position vectors d = 130i - 40j + 20k and e = 90i - 20j + 15k, and F is a point on the ski-slope.

i) Find the equation of the straight line DE.

This equals r = (130i - 40j + 20k) + λ(8i - 4j + k), as far I can see.
But then part ii)...

ii) Find the position vector of the point F.

I'm at a loss, any help is much appreciated!


I think the ski slope is described in
https://www.thestudentroom.co.uk/showthread.php?t=5444632
so you just need to find where the line DE intersects with the ski slope at point F, i.e. find the value of lambda.
Reply 3
Original post by black1blade
F is a general point on slope so if you had to express it algebraically, how would you?


Okay... I see now; point F is the point of intersection between line DE and the plane, so point F must satisfy the equation of the plane (2x-3y+7z=-5)
Then working it out, λ=15, and I get point F=(10,20,5).

Thanks a ton for the help!!
Reply 4
Original post by mqb2766
I think the ski slope is described in
https://www.thestudentroom.co.uk/showthread.php?t=5444632
so you just need to find where the line DE intersects with the ski slope at point F, i.e. find the value of lambda.


Thank you :smile:
F is the intersection of a line and a plane.... this is a standard vector problem..... you replace the r in the plane formula with the r from the line formula and find lambda.

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