If `p+q+r=0` and `|(pa,qb,rc),(qc,ra,pb),(rb,pc,qa)| = lambda |(a,b,c),(c,a,b),(b,c,a)|` then `lambda =`

If p + q + r = a + b + c = 0, then the determinant |{:(pa,qb,rc),(qc,ra,pb),(rb,pc,qa):}| equals

If |{:(a-b,b-c,c-a),(x-y,y-z,z-x),(p-q,q-r,r-p):}|=m|{:(c,a,b),(z,x,y),(r,p,q):}|," then m"=

If a,b,c are in AP and (a+2b-c)(2b+c-a)(c+a-b)=lambdaabc , then lambda is

Delta=|{:(p,q,r),(p+2a,q+2b,r+2c),(a,b,c):}| then

If p+q+r=0=a+b+c , then the value of the determinant |[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

If |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to :

a!=p , b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 the value of p/(p-a)+q/(q-b)+r/(r-c)=

If |(a^2,b^2,c^2),((a+lambda)^2,(b+lambda)^2,(c+lambda)^2),((a-lambda)^2,(b-lamda)^2,(c-lambda)^2)|=klambda|(a^2,b^2,c^2),(a,b,c),(1,1,1)|lambda!=0 then k is equal to : (A) 4 lambda abc (B) -4 lambda abc (C) 4 lambda^2 (D) -4 lambda^2

Without, prove that : |{:(1+b,b+c,c+a),(p+q,q+r,r+p),(x+y,y+z,z+x),:}|=2|{:(a,b,c),(p,q,r),(x,y,z):}|

If a+b+c=1 and a, b, c are positive real numbers such that (1-a)(1-b)(1-c)gelambda" abc, then "lambda =