Find the position vector of the points which divide the join of the points `5veca-4vecb` and `4veca-5vecb` internally and externally in the ratio 4:3 respectively.

Explanation

Let A and B be the given points with position vectors `5veca-4vecb` and `4veca-5vecb` respectively. Let P and Q be the points dividing AB in the ratio 4:3 internally and externally respectively. Then,
Position vector of P`=(3(5veca-4vecb)+4(4veca-5vecb))/(4+3)`
`=(31)/(7)veca-(32)/(7)vecb`
Position vector of Q `=(3(5veca-4vecb)-4(4veca-5vecb))/(3-4)`
`=(15veca-12vecb-16veca+20vecb)/(-1)`
`=(-veca+8vecb)/(-1)=veca-8vecb`