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# Position vectors with ratio watch

1. 2. The points A and B have position vectors 3i − 2j + k and −i + 2j − 7k.
Find position vector of the point P on AB such that
AP : P B = 3 : 1
2. (Original post by sk9898)
2. The points A and B have position vectors 3i − 2j + k and −i + 2j − 7k.
Find position vector of the point P on AB such that
AP : P B = 3 : 1
What have you done so far? Do you have a method for this?
3. (Original post by ghostwalker)
What have you done so far? Do you have a method for this?
ive worked out what AB is
4. (Original post by sk9898)
ive worked out what AB is
Good. So, what fraction of the way along AB is P going to be?
5. (Original post by ghostwalker)
Good. So, what fraction of the way along AB is P going to be?
3/4
6. (Original post by sk9898)
3/4
Yep. So AP = (3/4) AB

Then the position vector of P, that is OP, is simply OA + AP.
7. (Original post by ghostwalker)
Yep. So AP = (3/4) AB

Then the position vector of P, that is OP, is simply OA + AP.
so we do the opposite and add
8. (Original post by sk9898)
so we do the opposite and add
I can't interpret that sentence in any meaningful way. You'll have to elaborate on what you mean.
9. (Original post by sk9898)
so we do the opposite and add
final answer i got is j-5k or 0i+j-5k
10. (Original post by sk9898)
final answer i got is j-5k or 0i+j-5k
Agreed.
11. (Original post by ghostwalker)
Agreed.
thanks.

there is another question that i need help with.

Given three nonzero vectors a, b and c, are the following statements True or False? Give a short reason or counter-example to justify your answer.
(a) If a ⊥ b and also b ⊥ c then a ⊥ c.
(b) If a ⊥ b and also a ⊥ c then a ⊥ (b + c).
(c) If a ⊥ b and also b ⊥ c then b ⊥ (a − c).
(d) If a ⊥ (b + c) and also a ⊥ (b − c) then a ⊥ b.
12. (Original post by sk9898)
thanks.

there is another question that i need help with.

Given three nonzero vectors a, b and c, are the following statements True or False? Give a short reason or counter-example to justify your answer.
(a) If a ⊥ b and also b ⊥ c then a ⊥ c.
(b) If a ⊥ b and also a ⊥ c then a ⊥ (b + c).
(c) If a ⊥ b and also b ⊥ c then b ⊥ (a − c).
(d) If a ⊥ (b + c) and also a ⊥ (b − c) then a ⊥ b.
Have to leave that for someone else, as I've other things to be doing, and that's going to take a while. Do post your thoughts, what you've tried, etc. as per the forum guidelines.

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