`|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x,x+y+z):}|=2(x+y)(y+z)(z+x)`

|{:(a+x," "y," "z),(" "x,a+y," "z),(" "x," "y,a+z):}|=a^2(a+x+y+z)

Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

A person travels three equal distances at a speed of x km/hr, y km/hr and z knyhr respectively. What is the average speed for the whole journey? (x y z)/(3(x y+y z+z x)) b. (x y z)/((x y+y z+z x)) c. ((x y+y z+z x))/(x y z) d. (3x y z)/((x y+y z+z x))

What should be added to x y+y z+z x to get x y-y z-z x ? -2x y-2y z-2z x (b) -3x y-y z-z x -3x y-3y z-3z x (d) 2x y+2y z+2z x

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

Prove that |(y+z, x,y),(z+x, z, x),(x+y, y, z)| = (x+y+z)(x-z)^(2) .

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3