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  • Find the ratio in which the line joining the points (1 , 2 ,3 ) and (-3 , 4 , -5) is divided by the xy- plane . Also , find the coordinates of the point of division .

Find the ratio in which the line joining the points (1 , 2 ,3 ) and (-3 , 4 , -5) is divided by the xy- plane . Also , find the coordinates of the point of division .

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Solution:  Suppose the line segment joining the points P(1 , 2 3 ) and Q (-3 , 4 , -5 ) is divided by the xy - plane at a point  R    in the ratio lambda:1 . Then , the coordinates of  R are 

 i.e.           (frac-3lambda+1lambda+1, frac4lambda+2lambda+1, frac-5lambda+3lambda+1) ...............................(1)

Since  R lies on xy-plane  i.e.  Z = 0 . Therefore , z-coordinate of   R  must be zero . 

i.e.          frac-5lambda+3lambda+1=0Rightarrow lambda=frac35

So , the required ratio is        frac35:1     or   3:5 . 

Putting  lambda =frac35   in  (1)    , we obtain the coordinates of R as (-frac12 , frac114 , 0)

Posted by

Deependra Verma

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