IIT JEE , AIEEE Forum - Mathematics , Vectors

gaurav_2351

if pth qth rth term of a G.P. are the +ve no.s a b c then angle between the vectors log a^3 i + log b^3 j + log c^3 k and (q-r)i + (r-p)j + (p-q)k is?

pink_ele

log a^3 i + log b^3 j + log c^3 k =3(loga i +logb j+ logc k)
n
(q-r)i + (r-p)j + (p-q)k
u must be knwing 4 such a condition
(q-r)log a(r-p)+ log b+(p-q)log c=0
dis means
l1l2+m1m2+n1n2=0
i e vectors r perpendicular
angle =90 deg

varshavallig

even if u dunno the condition stated by pink_ele then do this:
a=AR^p-1
b=AR^q-1
c=AR^r-1
substitute these for a,b,c in the eqn 3((q-r)loga+(r-p)logb+(p-q)logc)
use property of log and take logAR outside.u will get it as 0.
so angle is 90'.
pink_ele is right
!!!!!!!!!!!!!!!!

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