Find the value of : `|(1+x,y,z),(x,1+y,z),(x,y,1+z)|`

Factorise : |(1,1,1),(x,y,z),(x^3,y^3,z^3)|

Factorise : |(1,1,1),(x,y,z),(x^2,y^2,z^2)|

Find the values of x, y, z and w if [(x,3x-y),(2x+z,3y-w)]=[(3,2),(4,7)]

Without expanding show that : |(x-y,y-z,z-x),(y-z,z-x,x-y),(z-x,x-y,y-z)|=0

If sin^(-1) x +sin^(-1)y +sin^(-1) z =(3pi)/(2) , then find the value of x^(100) +y^(100) +z^(100) -(9)/(x^(101)+y^(101)+z^(101)) .

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

Consider the following parallelograms. Find the values of the unknowns x, y, z.

Consider the following parallelograms. Find the values of the unknowns x, y, z.

Consider the following parallelograms. Find the values of the unknowns x, y, z.

Consider the following parallelograms. Find the values of the unknowns x, y, z.