In a `DeltaABC,` if `r_(1)=2r _(2)=3r_(3),` then show that `a/b=5/4.`

In a triangle, if r_(1) gt r_(2) gt r_(3), then show a gtb gt c.

If r_(1),r_(2) and r_(3) are the position vectors of three collinear points and scalars l and m exists such that r_(3)=lr_(1)+mr_(2) , then show that l+m=1.

In DeltaABC, let b=6, c=10and r_(1) =r_(2)+r_(3)+r then find area of Delta ABC.

The distance between two particles of masses m_(1)andm_(2) is r. If the distance of these particles from the centre of mass of the system are r_(1)andr_(2) respectively, then show that r_(1)=r((m_(2))/(m_(1)+m_(2)))andr_(2)=r((m_(1))/(m_(1)+m_(2)))

If both (x-2) and (x - (1)/(2)) are fractors of p x ^(2)- 5x +r, then show that p=r.

Let A = R - {3} , B = R - {1} . If f : A rarr B be defined f(x) = (x-2)/(x-3) AAx inA . Then show that f is bijective.

In a triangle ABC I_1, I_2,I_3 are excentre of triangle then show that II_(1). II_(2). II_(3)=16R^(2)r.

omega is the cube root of 1 and omega ne 1 . Now r_(1), r_(2) and r_(3) are the number obtained while tossing dice thrice. Then ………… is the probability for omega^(r^(1)) +omega^(r^(2))+omega^(r^(3))=0

Statement I In a Delta ABC, if a lt b lt c and ri si inradius and r_(1), r_(2) ,r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

Six resistances each of v ale r= 6Omega are connected between points A,B and C as shown in the figure if R_(1),R_(2) and R_(3) are the net resistances between A and B, between B and C and between A and C respectively, the R_(1):R_(2):R_(3) will be equal to