If the positive numbers a, b and c are the pth, qth and rth terms of GP, then the vectors `(loga) hati+(logb) hatj+(logc) hatk and (q-r)hati+(r-p)hatj+(p-q) hatk ` are

If a, b,c are the pth, qth, and rth terms of a HP, then the vectors vecu= hati/a + hatj/b + hatk/c and vecv = ( q -r) hati + ( r-p) hatj + ( p-q) hatk

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 a, b,c are the pth, qth, and rth terms of a HP, then the vectors vecu= a^(-1) hati +b^(-1) hatj +c^(-1) hatk and vecv = ( q -r) hati + ( q -r) hati + ( r-p) hatj + ( p-q) hatk

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

If a,b,c be the pth , qth and rth terms of an A.P., then p(b-c) + q(c-a) + r(a-b) equals to :

If a,b,c are respectively the pth ,qth and rth terms of a G.P. then (q-r) log a +(r-p) log b+(p-q) log c=