Grade 12Analytical Geometry

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

Tapasranjan Das

16 Years agoGrade 12

1 Answer

Badiuddin askIITians.ismu Expert

16 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

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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