# A vectors problem

1. Jun 27, 2012

### manmachine

1. The problem statement, all variables and given/known data

X divides a line segment (AB) in a ratio of 3:4. Y divides line segment AX in a ratio of 1:2.
If K is any point of the line containing A,B,X and Y; Please show that AY= 1/7OB - 1/7OA

2. Relevant equations
Not sure if any. Just adding and subtracting vectors.

3. The attempt at a solution

Alright so I know that 1/4 AB +BO would equal XO, but i don't know what do next. Thanks for the help.

2. Jun 27, 2012

### tiny-tim

hi manmachine!
do you mean "If O is any point of the line containing A,B,X and Y; Please show that AY= 1/7OB - 1/7OA" ?

hint: what is OB - OA ?

3. Jun 27, 2012

### 106267

This has nothing to do with the quesiton but how do i ask question on this forum?

4. Jun 27, 2012

### tiny-tim

welcome to pf!

hi 106267! welcome to pf!
here's something i've been drafting … (some of the opinions are my own)

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2. Relevant equations

3. The attempt at a solution

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5. Jun 27, 2012

### manmachine

It is AB? I don't know what to do next!

6. Jun 27, 2012

### tiny-tim

yes!

ok, so now all you need to prove is AY = 1/7 AB

7. Jun 27, 2012

### manmachine

And then what next?? I know, I know, I know I ask so many questions. Shame on me. Had surgery so couldn't come to many lectures.

8. Jun 27, 2012

### tiny-tim

write that in vector equations …

what do you get?

9. Jun 27, 2012

### manmachine

Ab= ax+ xy?

10. Jun 27, 2012

### tiny-tim

uhh?

there's two equations

try this one first …

X divides a line segment (AB) in a ratio of 3:4​

11. Jun 27, 2012

### manmachine

So AX+XB=AB?

12. Jun 27, 2012

### tiny-tim

well, yes, but that is true wherever X is, isn't it?

you need an equation with 3 and 4 (or 7) in !!

13. Jun 27, 2012

### manmachine

How can I do that? What is it? I am so bad at this :P

14. Jun 27, 2012

### HallsofIvy

Staff Emeritus
First, in your original post you said "If K is any point of the line containing A,B,X and Y; Please show that AY= 1/7OB - 1/7OA" which makes no sense. tiny-tim, in his first response, asked if you meant "O" rather than "K" but you never answered. tiny-tim proceeded to assume you meant "O".

Here's how I would do this problem. Let "A" be "0" on a number line. Since 3+ 4= 7, take "B" to be "7" on that same number line. That choice makes "X divides a line segment (AB) in a ratio of 3:4" easy: "X" is at the number "3" on that number line.- AX= 3 and XY= 4, a ratio of 3:4. And "Y divides line segment AX in a ratio of 1:2" is also easy: "Y" is at the number "1"- AY= 1 and YX= 2 so the ratio is 1:2.

Let "O" be any point on that number line, at, say "z". Then OB is |z- 7| and OA is |z|. We have already seen that AY= 1. Do the algebra.

15. Jun 27, 2012

### tiny-tim

"X divides a line segment (AB) in a ratio of 3:4"​

manmachine, what does that mean in ordinary english?