`P`and `Q`are twopoints with position vectors `3 vec a-2 vec b`and ` vec a+ vec b`respectively. Write theposition vector of a point R which divides the line segment PQ in the ratio2:1 externally.

`P`and `Q`are twopoints with position vectors `3 vec a-2 vec b`and ` v

1.	`P`and `Q`are twopoints with position vectors `3 vec a-2 vec b`and ` vec a+ vec b`respectively. Write theposition vector of a point R which divides the line segment PQ in the ratio2:1 externally.
Answer» The position vectors of the given points are `P(3veca - 2vecb)` and `Q(veca+vecb)` We have to divide PQ in the ratio `2:1` externally at the points R. The position vector of R is `(2(veca+vecb)-1.(3veca-2vecb))/((2-1)) = (-veca+4vecb)`. Hence, the position vector of `R` is `(-veca + 4vecb)`.

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