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Write the Position Vector of the Point Which Divides the Join of Points with Position Vectors - Mathematics

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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