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Find the position vectors of the points which divide the join of the points `2 vec a-3 vec ba n d3 vec a-2 vec b` internally and externally in the ratio `2:3` .

Text Solution

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Let P be a point which divide AB internally in the ratio 2:3, then, by section formula, poistion vector of P is given by
`OP=(2(3a-2b)+3(2a-3b))/(2+3)`
`=(6a-4b+6a-9b)/(5)=(12)/(5)a-(13)/(5)b`
Similarly, the position vector of the point `(P')` which divided AB externally in the ratio 2:3 is given by
`OP'=(2(3a-2b)-3(2a-3b))/(2-3)`
`=(6a-4b-6a+9b)/(-1)=(5b)/(-1)=-5b`
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