The minimum value of `P=b c x+c a y+a b z ,` when `x y z=a b c` , is

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

If (x)/(b + c - a) = (y)/(c + a - b) = (z)/(a + b - c) , then value of x(b -c) + y(c -a) + z(a - b) is equal to

If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x, a+p], [q+y ,b+y, b+q],[ x+z, c+z, c+r]| is 4 (b) 8 (c) 16 (d) 32

Show that |a b c a+2x b+2y c+2z x y z|=0

If x+a=y+b+1=z+c then the value of [[x, (a+y), (a+x)], [y, (b+y), (b+y)], [z, (c+y), (c+z)]] is

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|