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Tapasranjan Das Grade: 12
        

Q:-Let the points A9a,b,c) and B(d,e,f) be at distances p and q from origin. The line AB passes through origin when


A. (d/a)=(e/b)=(f/c)


B. ad+be+cf=pq


C. ad+be+cf=p2+q2


D. None of these

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Tapasranjan


AB line passes through origin so slope of line joining the origin and A  , and slope of line joining the origin and B will be same


d-0 /a-0   = e-0 /b-0   = f-0 /c-0


or


 d/a = e/b  =f/c = k   .....................1


option a is correct


now use distance formula


a2 +b2+ c2 = p2   


and


d2 + e2 + f2 =q2


now


 put value of d,e,f in terms of a,b,c


 k2 ( a2 +b2+ c2 ) = q2 


 k2 ( p2 ) = q2  


 k = q/p




now let  ad +eb + fc


          = k(a2 +b2+ c2 )


          =q/p  ( p2)


          =pq


  option b is also correct


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Badiuddin

7 years ago
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