if `bc+ qr= ca+rp = ab+ pq =-1` then prove that
`|{:(ap,,a,,p),(bq,,b,,q),(cr,,c,,r):}|=0`

If bc+qr=ca+rp=ab+pq=-1 and (abc,pqr!=0) then |[ap,a,p],[bq,b,q],[cr,c,r]| is (A) 1 (B) 2 (C) 0 (D) 3

If p^(th), q^(th),r^(th) terms an A.P are 1/a,1/b and 1/c respectively prove that Delta=|(bc,ca,ab),(p,q,r),(1,1,1)|=0

Without expanding at any state, prove that |((1)/(a),a,bc),((1)/(b),b,ca),((1)/(c ),c,ab)|=0

Without expanding at any state, prove that |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b))|=0

If a+b+c=5 and ab+bc+ca=10, then prove that a^(3)+b^(3)+c^(3)-3abc=-25 .

If a+b+c=5 and ab+bc+ca=10 , then prove that a^3+b^3+c^3-3abc=-25 .

If AB=QR , BC=PR and CA=PQ then

If a,b,c are in H.P and ab+bc+ca=15 then ca=

If a,b,c be the pth, qth and rth terms respectively of a H.P., the |(bc,p,1),(ca,q,1),(ab,r,1)|= (A) 0 (B) 1 (C) -1 (D) none of these

If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then