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  • Find the ratio in which join the A(2 , 1 , 5 ) and B(3, 4 , 3) is divided by the plane 2x+2y-2z=1 . Also , find the coordinates of the point of division .

Find the ratio in which join the A(2 , 1 , 5 ) and B(3, 4 , 3) is divided by the plane 2x+2y-2z=1 . Also , find the coordinates of the point of division .

Answers (1)

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Solution:  Suppose the plane 2x+2y-2z=1 divides the line joining the points A(2 , 1 , 5) 

               and B(3,4,3) at a point C in the ratio lambda :1 . Then the  coordinates of C are 

                              (frac3lambda+2lambda+1 , frac4lambda+1lambda+1 , frac3lambda+5lambda+1)    ................................(1)

Since point C lies on the plane 2x+2y-2z=1 . Therefore, coordinates of C must satisfy the 

equation of the plane 

i.e.         2(frac3lambda+2lambda+1) + 2(frac4lambda+1lambda+1) -2(frac3lambda+5lambda+1)=1 Rightarrow 8lambda-4 =lambda+1Rightarrow lambda=frac57

So , the required ratio is frac57:1  or 5:7 .

Putting lambda=frac57 in (1) , the coordinates of the point of division C are (frac2912, frac94,frac256).

Posted by

Deependra Verma

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