Solve for y: Find Ratio of E Dividing CA in Triangle AOB

[ritwik06]

Homework Statement

There is a triangle(AOB). One of its median is drawn. BO is divided in the ratio 2:1. The resultant point(say C) is joined with the vertex A. Find the ratio (y) in which E divides CA .

http://img88.imageshack.us/img88/8496/vectorszx0.png

The Attempt at a Solution

Let O b the origin an the position vectors of A and b are $$\vec{a}$$ and $$\vec{b}$$.
Let the median meet OA at D. Position vector of d=$$\vec{a/2}$$
Position vector of C=$$\vec{b/3}$$
Let E divide BD in ratio x:1
equating the coordinates of e
$$\frac{x\vec{a/2}+\vec{b}}{x+1}=\frac{y\vec{b/3}+\vec{a}}{y+1}$$

What I need is more equation to solve for y! Please Help me!

 

[tiny-tim]

$$\frac{x\vec{a/2}+\vec{b}}{x+1}=\frac{y\vec{b/3}+\vec{a}}{y+1}$$

What I need is more equation to solve for y!

Hi ritwik06!

(on this forum, its easier if you use bold for vectors, than arrows )

No, all you need to do is to split it into two equations, one for a and one for b.

Remember, a and b are independent, so if pa + qb= 0, then p = q = 0.

 

[ritwik06]

hi ritwik06!

(on this forum, its easier if you use bold for vectors, than arrows )

no, all you need to do is to split it into two equations, one for a and one for b.

Remember, a and b are independent, so if pa + qb= 0, then p = q = 0.

SOLVED
thanks a lot.