Proving Collinearity and Segment Division in Vector Multiplication

[crayzwalz]

Homework Statement

If OA = 1/3OB + 2/3OC, then prove that A, B, and C are collinear and that A divides the segment BC in the ratio 2:1.

Homework Equations

OA = 1/3 OB + 2/3OC
A divides segment BC into 2/3s

The Attempt at a Solution

I don't know where to start on this question.



P.S. I'm not looking for a solution (although that wouldn't hurt), just a way on how to start solving these solutions. I am very bad at "proving" stuff.

 

[berkeman]

Homework Statement

If OA = 1/3OB + 2/3OC, then prove that A, B, and C are collinear and that A divides the segment BC in the ratio 2:1.

Homework Equations

OA = 1/3 OB + 2/3OC
A divides segment BC into 2/3s

The Attempt at a Solution

I don't know where to start on this question.



P.S. I'm not looking for a solution (although that wouldn't hurt), just a way on how to start solving these solutions. I am very bad at "proving" stuff.

Is there a figure that goes with this question? Or can you draw one to help us understand what the issue is?

 

[Quinzio]

I don't know where to start on this question.

If A,B and C are collinear, what can you say about vectors AB and AC ?

 

[crayzwalz]

There was no figure given.

and vectors AB = 2/3AC?

 

[Quinzio]

Wait.
You're give 3 collinear points A B C you don't know nothing else.

Tell me something about vectors AB and AC.

Draw them on a piece of paper.

 

[crayzwalz]

so i googled it and their parallel, go head to tail and multiples of each other?

 

[Quinzio]

Ok, so to transform one vector into a parallel vector I multiply it by a ?

 

[crayzwalz]

i honestly don't know lol