Question

In a `triangle OAB`,E is the mid point of OB and D is the point on AB such that `AD:DB=2:1` If OD and AE intersect at P then determine the ratio of `OP: PD` using vector methods

Answer 1

`P=((lambda/2)vecb+veca)/(lambda+1)`
`P=Y vec(OD)`
`=Y(2/3vecb+veca/3)`
`(lambda)/(2(lambda+1)vecb)+1/(lambda+1)veca=2/3Yvecb+Y/3veca`
`Y/3=1/(lambda+1)`
`lambda/(2(lambda+1))=2/3Y`
`lambda/2(1/(lambda+1))=2/3*3/(lambda+1)`
`lambda=4`
`Y=3/5`
`vec(OP)=3/5vec(OD)`.