If `z=x+i y, z^(1/3)=a-i b " and " x/a-y/b=lambda(a^2-b^2),` then `lambda` is equal to

If z=x+i y, z^(1 / 3)=a-i b and (x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then the value of k=

If the distance between the plane 23x-10y-2z+48 =0 and the plane containing the lines (x+1)/2 =(y-3)/4= (z+1)/(3) and (x+3)/(2)=(y+2)/6 = (z-1)/(lambda)(lambda in R) is equal to k/sqrt(633) , then k is equal to __________.

If the distance between the plane 23x-10y-2z+48 =0 and the plane containing the lines (x+1)/2 =(y-3)/4= (z+1)/(3) and (x+3)/(2)=(y+2)/6 = (z-1)/(lambda)(lambda in R) is equal to k/sqrt(633) , then k is equal to __________.

If x=(4 lambda)/(1+lambda^(2)) and y=(2-2 lambda^(2))/(1+lambda^(2)) where lambda is a real parameter and Z=x^(2)+y^(2)-xy then possible values of Z can be

If the line (x-1)/(1)=(y-k)/(-2)=(z-3)/(lambda) lies in the plane 3x+4y-2z=6 , then 5|k|+3|lambda| is equal to