Find the value of the determinant `|b cc a a b p q r1 1 1|,w h e r ea ,b ,a n dc` are respectively, the pth, qth, and rth terms of a harmonic progression.

The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]|,w h e r ex ,y ,z are respectively, pth, (2q) th, and (3r) th terms of an H.P. is a. -1 b. 0 c. 1 d. none of these

Solve the equation |a-x c b c b-x a b a c-x|=0w h e r ea+b+c!=0.

If a, b and c are respectively the p^(th) , q^(th) and r^(th) terms of an A.P., then |(a" "p" "1),(b" "q" "1),(c" "r" "1)|=

Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

Find the value of lambda so that the points P ,Q ,R and S on the sides O A ,O B ,OC and A B , respectively, of a regular tetrahedron O A B C are coplanar. It is given that (O P)/(O A)=1/3,(O Q)/(O B)=1/2,(O R)/(O C)=1/3 and (O S)/(A B)=lambdadot (A) lambda=1/2 (B) lambda=-1 (C) lambda=0 (D) for no value of lambda

If p+q+r=0=a+b+c =0, then the value of the determnalnt |p a q b r c q c r a p b r b p c q a|i s a 0 b. p a+q b+r c c. 1 d. none of these

Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q (r-p) +c/r (p-q)=0

If a,b,c are pth , qth and rth terms of an A.P., find the value of |(a,b,c),(p,q,r),(1,1,1)|