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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. |
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Answer» Let `P(-2,3,5) ` and `Q(1,-4,6)` are the given points and we have to find coordinates of point `R(x,y,z)`. (i) Coordinates of a point which divides the line internally in ratio `m:n` are given by `((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n),(mz_2+nz_1)/(m+n))` Here, `m:n` = `2:3`. So, `R(x,y,z) = ((2(1)+3(-2))/(2+3),(2(-4)+3(3))/(2+3),(2(6)+3(5))/(2+3))` `= (-4/5,1/5,27/5)` (ii)Coordinates of a point which divides the line externally in ratio `m:n` are given by `((mx_2-nx_1)/(m-n),(my_2-ny_1)/(m-n),(mz_2-nz_1)/(m-n))` Here, `m:n` = `2:3`. So, `R(x,y,z) = ((2(1)-3(-2))/(2-3),(2(-4)-3(3))/(2-3),(2(6)-3(5))/(2-3))` `= (-8,17,3)`. |
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