Find `vecgrad . vecF`, where `vecF= vecgrad(x^3+y^3+z^3-3xyz)`

Factorise : 27x^(3)+8y^(3)+8z^(3)-36xyz

Divide 30x^(2)y^(3)z by -3xyz

A vector vecF_(1) is along the positive X -axis. its vectors product with another vector vecF_(2) is ? where vecF_(2) is along Y-axis

If x=1,\ y=-2\ a n d\ z=3, find the values of each of the following algebraic expressions: (i) x^3+y^3+z^3-3x y z (ii) 3x y^4-15 x^2y+4z

If x^(2)+y^(2)+z^(2)=1"for " x,y,z inR, then the maximum value of x^(3)+y^(3)+z^(3)-3xyz is

If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^3-3x y z

Using properties of determinants, prove that |{:(y + z ,z + x ,x + y ),(z + x ,x + y ,y + z),(x + y ,y + z,z + x ):}|=2 |{:(x, y, z),(y, z, x),(z, x, y):}|= - 2 (x^(3) + y^(3) + z^(3) - 3xyz)

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

A particle, in equilibrium, is subjected to four forces vecF_1, vecF_2, vecF_3 and vecF_4 , vec F_1 =-10 hat k , vec F _2 =u(4/13 hat i-12/13 hat j+3/13 hatk) , vec F _3 =v(-4/13 hat i-12/13 hat j+3/13 hatk), vec F_4 =w(cos theta hat i+sin theta hat j) then find the values of u,v and w

Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3