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P ,Q have position vectors vec a& vec b...

`P ,Q` have position vectors ` vec a& vec b` relative to the origin `' O^(prime)&X , Ya n d vec P Q` internally and externally respectgively in the ratio `2:1` Vector ` vec X Y=` `3/2( vec b- vec a)` b. `4/3( vec a- vec b)` c. `5/6( vec b- vec a)` d. `4/3( vec b- vec a)`

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Since, X and Y divide PQ internaly and exteranally in the ratio 2:1 then `X=(2b+a)/(3) and y=2b-a`
`thereforeXY=`Position vector y-position vector off x
`=2b-a-(2b+a)/(3)=(4b)/(3)-(4a)/(3)`
On comparing it with `lamda a+mub`, we get
`lamda=-(4)/(3) and mu=(4)/(3)`
`therefore|lamda+mu|=|(-4)/(3)+(4)/93)|=0`
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