AP EAMCET Engineering 2012 Solved Paper

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=

π

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