If ` vec aa n d vec b` are position vectors of `Aa n dB` respectively, find the position vector of a point C on B A produced such that `B C=1. 5B Adot`

Explanation

Since, `vec(AO)=vecaandvec(OB)=vecb`
`:.vec(BA)=vec(OA)-vec(OB)=veca-vecb`
and `1.5vec(BA)=1.5(veca-vecb)`
Since`vec(BC)=1.5vec(BA)=1.5(veca-vecb)`
`vec(OC)-vec(OB)=1.5veca-1.5vecb`
`vec(OC)=1.5veca-1.5vecb+vecb " "[":.vec(OB)=vecb"]"`
`=1.5veca-0.5vecb`
`=(3veca-vecb)/(2)`
Graphically, explanation of the above solution is given below