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

Explanation

(i) Let R(x, y, z) be the required point which divides line segment joining A(1, 5, 3) and B(-2, 3, 4) internally in the ratio 3:4.
`therefore x = (3xx(-2)+4xx1)/(3+4) =(-2)/7`
`y=(3xx3+4xx5)/(3+4)=29/7`
`z=(3xx4+4xx5)/(3+4)=24/7`
Thus, the required point is `((-2)/7, 29/7,24/7).`

(ii) Let P(x, y, z) be the required point which divides the line segment joining A(1, 5, 3) and
B(-2, 3, 4) externally in the ratio `3 : 4` then
`therefore x= (3xx(-2)-4xx1)/(3-4) =10`
y= (3xx3-4xx1)/(3-4) =11`
x= (3xx4-4xx1)/(3-4) = 0`
`therefore` The required point is (10, 11, 0).