Find the coordinates of the point which divides the line segment joining the points `( 2, 3, 5)`and `(1, 4, 6)`in the ratio (i) `2 : 3`internally, (ii) `2 : 3`externally.

Answer

N/a

Explanation

Let point (x,y,z) divides the line segment joining the points A(-2,3,5) and B(1,-4,6) in the ratio 2 : 3 internally.
`therefore x=(mx_(2)+nx_(1))/(m+n)`
`=(2(1)+3(-2))/(2+3)=(-4)/(5)`
`y=(my_(2)+ny_(1))/(m+n)=(2(-4)+3(3))/(2+3)=(1)/(5)`
`z=(mz_(2)+nz_(1))/(m+n)=(2(6)+3(5))/(2+3)=(27)/(5)`
` therefore " Coordinates of required point " =((-4)/(5),(1)/(5),(27)/(5))`
(ii) Let point Q(x,y,z) divides the line segment joining the points A(-2,3,5) and B(1,-4,6) in the ratio 2 : 3 externally.
`therefore x=(mx_(2)-nx_(1))/(m-n)=(2(1)-3(-2))/(2-3)= -8`
`y=(my_(2)-ny_(1))/(m-n)=(2(-4)-3(3))/(2-3)=17`
`z=(mz_(2)-nz_(1))/(m-n)=(2(6)-3(5))/(2-3)=3`
`therefore ` Coordinates of required point=(-8,17,3)