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Question
Write the position vector of the point which divides the join of points with position vectors `3veca-2vecb and 2veca+3vecb` in the ratio 2 : 1.
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Solution
Suppose R be the point which divides the line joining the points with position vectors `3veca-2vecb and 2veca+3vecb` in the ratio 2 : 1.
and `vec(OA)=3veca-2vecb and vec(OB)=2veca+3vecb`
Here, m : n = 2 : 1
Therefore, position vector `vec(OR)` is as follows
`vec(OR)=(mvec(OB)+nvec(OA))/(m+n)`
`=(2(2veca+3vecb)+1(3 veca-2 vecb))/(2+1)`
`=(7 vec a+4vecb)/3`
`=7/3 veca+4/3 vec b`
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