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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 when
A. (d/a)=(e/b)=(f/c)
B. ad+be+cf=pq
C. ad+be+cf=p2+q2
D. None of these
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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