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Anurag Kishore Grade: 12
        

Sir,


We know that whenever two planes intersect, they intersect in a line.


How to find the equation of that line?


 


 


Very urgent please reply soon

7 years ago

Answers : (1)

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
										

Dear Anurag Kishore,


Ans:- Let the two planes be


 A1x +B1y +C1z=D1................(1)


A2x+B2y+C2z=D2..................(2)


Now the Direction ratioes normal to the line


(1) are A1 B1 C1...........(3)


(2) are A2 B2 C2.........(4)


now by taking cross product of (3) & (4) we get the vector Q parallel to the required line.


Now the equation of the line is r=P+λQ


where We have got Q. But To find P i.e a point on the line let's consider point a,b,c which lie on the line and hence must satisfy both the equations (1) & (2) So,


A1a+B1b+C1c=D1............(5)


A2a+B2b+C2c=D2............(6)


Now eliminate one variable to make an equation of 2 variables say a & b.


Now by hit and trial method find one pair of a,b satisfying that equation then from it find c also.


So we now have one set of (a,b,c)


So we can find the line.


N.B:- The hit and trial method we have used because there will not be one and only fixed point on the line through which it is passing through.


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All the best Anurag Kishore !!!


 



Regards,


Askiitians Experts
Soumyajit Das IIT Kharagpur

7 years ago
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