[" If "p^(th),q^(th),r^(th)" terms of a G.P.are the positive numbers a,"b,c" then angle between the vector "],[log a^(3)bar(i)+log b^(3)bar(j)+log c^(3)bar(k)" and "(q-r)bar(i)+(r-p)bar(j)+(p-q)bar(k)" is "]

If p^(th),q^(th),r^(th) terms of a G.P. are the positive numbers a,b,c then angle between the vectorslog log a^(3)bar(i)+log b^(3)bar(j)+log c^(3)nbar(k) and (q-r)bar(i)+(r-p)bar(j)+(p-q)bar(k) is

If p^(th), q^(th), r^(th) , terms of a G.P. are the positive numbers a, b, c respectively then angle between the vectors log a^3 hat i + log b^3 hatj + log c^3 hatk and (q - r)hati + (r - p)hatj + (p - q) hatk is:

If p^(th), q^(th), r^(th) , terms of a G.P. are the positive numbers a, b, c respectively then angle between the vectors log a^3 hat i + log b^3 hatj + log c^3 hatk and (q - r)hati + (r - p)hatj + (p - q) hatk is: (a) pi/2 (b) pi/3 (c) 0 (d) sin^(-1)""(1)/(sqrt(p^2 + q^2 + r^2))

If p^(th), q^(th), r^(th) terms of a geometric progression are the positive numbers a,b,c respectively, then the angle between the vectors (log a^(2)) I + (log b^(2)) j + (log c^(2))k and (q - r) I + (r - p) j + (p - q) k is

If p^(th), q^(th), r^(th) terms of a G.P are a,b,c then Sigma (q-r) log a=

If a,b,c are the p^("th") , q^("th") and r^("th") terms of G.P then the angle between the vector vecu = (log a) hati + (log b)hatj + (log c) hatk and vecv -( q -r) hati + ( r -p) hati + ( r-p) hatj + ( p-q) hatk , is

If a,b,c are the p^("th") , q^("th") and r^("th") terms of G.P then the angle between the vector vecu = (log a) hati + (log b)hatj + (log c) hatk and vecv -( q -r) hati + ( r -p) hati + ( r-p) hatj + ( p-q) hatk , is

The angle between the planes bar(r)*(2bar(i)-3bar(j)+4bar(k))+11=0 and "bar(r)*(3bar(i)-2bar(j))=0. is