Question

If `overlinea, overlineb, overlinec` are the position vectors of the points A, B, C respectively and `5overlinea + 3overlineb - 8overlinec = overline0` then find the ratio in which the point C divides the line segment AB.

Answer 1

`5overlinea + 3overlineb - 8overlinec = overline0`

∴ `8overlinec = 5overlinea + 3overlineb`

∴ `overlinec = (5overlinea + 3overlineb)/8`

∴ `overlinec = (5overlinea + 3overlineb)/(5 + 3)`

∴ As per the section formula for internal division,

Point C divides the line segment AB internally in the ratio 5 : 3