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, 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

Determinant (x-y)(y-z)(z-x)(x+y+z)

In the relation x > y+z , x+y > p a n d z p (b) x+y > z (c) y+p > x (d) insufficient data

For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z^2 ,1+p z^3]|=(1+p x y z)(x-y)(y-z)(z-x) .

The sides of triangle are denoted by x , y nd z . Area of the triangle and semiperimeter of the triangle are denoted by P and q respectively .If P= sqrtq (q-x)(q-y)(q-z) and x+y-z=y+z-x=z+x-y=4 Find P (in square units)

If the lattice point P(x, y, z) , x, y, zgto and x, y, zinI with least value of z such that the 'p' lies on the planes 7x+6y+2z=272 and x-y+z=16, then the value of (x+y+z-42) is equal to

If the lattice point P(x, y, z) , x, y, zgto and x, y, zinI with least value of z such that the 'p' lies on the planes 7x+6y+2z=272 and x-y+z=16, then the value of (x+y+z-42) is equal to

If the lattice point P(x, y, z) , x, y, zgto and x, y, zinI with least value of z such that the 'p' lies on the planes 7x+6y+2z=272 and x-y+z=16, then the value of (x+y+z-42) is equal to

If the lattice point P(x, y, z) , x, y, zgto and x, y, zinI with least value of z such that the 'p' lies on the planes 7x+6y+2z=272 and x-y+z=16, then the value of (x+y+z-42) is equal to

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these