" The doteminant "|[x+y,x,y],[y+z,y,z],[0,x+y,yp+z]|=0,1

The determinant |[x p+y, x, y], [y p+z, y, z],[0,x p+y, y p+z]|=0 if (a) x y z are in AP (b) x y z are in GP (c) x y z are in HP (d) xy yz zx are in AP

The determinant: |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 if :

Select and write the correct answer from the given alternatives in each of the following:The determinant |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 for all p in R if

The determinant |(xp+y, x, y),(yp+z, y , z),(0, xp+y , yp+z)|=0 , if

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

det [[xp + y, x, yyp + z, y, z0, xp + y, yp + z]] = 0 if

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .