`a^(p-q)`. `a^(q-r)`. `a^(r-p)` = _____________

Additional Bits: a!=0 , p+q+r = 0, a^(3p+3q+3r) = _____________

|(0,p-q,p-r),(q-p,0,q-r),(r-p,r-q,0)|=

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 the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

If pth, qth, rth terms of an A.P are a,b,c then a(q - r ) + b(r - p ) + c(p - q) =

(p rArr q) ^^ (q rArr r) rArr (p rArr r) is

If p^(th), q^(th), r^(th) terms of a H.P be respectively a, b and c then (q-r) bc + (r-p) ca + (p-q)ab =

For three vectors bar(p), bar(q) and bar(r)" if "bar(r)=3bar(p)+4bar(q) and 2bar(r)=bar(p)-3bar(q) then