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Find the ratio in which the line segment joining the points `(4, 8, 10)`and `(6, 10 , -8)`is divided by the YZplane. |
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Answer» Let `P(4,8,10) ` and `Q(6,10,-8)` are the given points and YZ plane divides the line segment joining these points in ratio `k:1`. 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))` So, `R(x,y,z) = ((k(6)+1(4))/(k+1),(k(10)+1(8))/(k+1),(k(-8)+1(10))/(k+1))` `=((6k+4)/(k+1),(10k+18)/(k+1),(-8k+10)/(k+1))` As this is divided by YZ plane, x-coordinate will be `0`. `:. (6k+4)/(k+1) = 0=> k = -2/3` So, required ratio is `2:3` and line segment is divided externally. |
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