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# 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 whenA. (d/a)=(e/b)=(f/c)B. ad+be+cf=pqC. ad+be+cf=p2+q2D. None of these Badiuddin askIITians.ismu Expert
148 Points
11 years ago

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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