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Question

In what ratio is the line segment joining the points (2,4,7) and (3,5,8) is divided by the YZ plane ?Also, find the co-ordinates of the point of division.

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Solution

Let the line segment formed by joining the points (2,4,7) and (3,5,8) is divided by the YZ plane in the ratio k:1 at the point P, then the co-ordinates of P are
(3k2k+1,5k+4k+1,8k+7k+1)
But P lies in the YZ plane,
xco-ordinate is zero
3k2k+1=0
3k2=0
3k=2
k=23
Hence,YZ plane divides the line segment AB in the ratio 23:1
i.e.,2:3 internally and the coordinates of the point of division are
⎜ ⎜ ⎜3×23223+1,5×23+423+1,8×23+723+1⎟ ⎟ ⎟
or ⎜ ⎜ ⎜222+33,10+1232+33,16+2132+33⎟ ⎟ ⎟
or ⎜ ⎜ ⎜0,2353,37353⎟ ⎟ ⎟
or (0,25,375)

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