1+ pr I py 1+ pz' Z) (z -x)

{:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(3)),( z,z^(2) , 1+pz^(3)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

{:|( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) |:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

Nitrogen has the electronic configuration '1 s^2 2 s^2 p_x^1 2 p_y^1 2 p_z^1' and not '1 s^2 2 s^2 2 p_x^2 2 p_y^1 2 p_z^0' which is determined by

If (logx)/(ry-qz) = (log y)/(pz - rx) = (log z)/(qx - py) , then prove that x^(p) . Y^(q) . Z^(r ) = 1 .