Let first term of a GP be u and common ratio z ∴Tp=uzp−1=a ⇒ logu+(p−1)logz=loga .......(i) Tq=uzq−1=b ⇒ logu+(q−1)logz=logb .......(ii) and Tr=uzr−1=c ⇒logu+(r−1)logz=logc ........(iii) Let θ be the angle between (loga2)i+(logb2)j+(logc2)k and (q−r)i+(r−p)j+(p−q)k is
From Eqs. (i), (ii) and (iii) q−r=logb−logc,r−p=logc−loga p−q=loga−logb ∴ From Eq. (iv), taking numerator term =2loga(logb−logc)+2logb(logc−loga)+2logc(loga−logb) =0 ∴ From Eq. (i), we get cosθ=0⇒θ=
