IIT JEE , AIEEE Forum - Mathematics , Algebra

twinkle_star

if pth , qth & rth terms of a GP are the positive no. a,b,c then the angle between the vetcors
loga²i + logb²j + logc²k & (q - r)i + (r - p)j + (p - q)k is?

twinkle_star

help in this 1 too please

raulrag009

Let

AR^p-1 = a , AR^q-1=b and AR^r-1=c

where A and R are the first term and common ratio of the G.P.

take log on both sides

u get

logA + (p-1)logR=loga....(1)

logA + (q-1)logR=logb.....(2)

logA + (r-1)logR=logc......(3)

subtract (3) from (2)

u get (q-r)=(logb-logc)/logR

subtract (1)from (3)

(r-p)=(logc-loga)/logR

and subtract (2) from (1)

(p-q)=(loga-logb)/logR

Substitute the values of (p-q), (r-p ) and (q-r) in the vector eqn.

take dot product between two vectors.

u get

2loga[(logb-logc)/logR] + 2logb[(logc-loga)/logR] + 2logc[(loga-logb)/logR]=0

thus cos@=0

thus angle will be pie/2

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