Find the co-ordinates of the point which divides the line segment joining the points (2,3,-4) and (4,-1,2) in the ratio (i) 2 : 3 internally, (ii) 4 : 3 externally.

Answer

N/a

Explanation

(i) Let the required point be (x,y,z).
`therefore x=(2xx4+3xx2)/(2+3)=(14)/(5)`
`y=(2xx(-1)+3xx3)/(2+3)=(7)/(5)`
`z=(2xx2+3xx(-4))/(2+3)=(-8)/(5)`

`therefore " Required point" =((14)/(5),(7)/(5),(-8)/(5))`.
(ii) Let the required point be (x,y,z).
`therefore x=(4xx4-3xx2)/(4-3)=10`
`y=(4xx(-1)-3xx3)/(4-3)=-13`
`z=(4xx2-3xx(-4))/(4-3)=20`

`therefore " Required point" =(10, -13, 20)`