`sin57^(@)cos3^(@)=(sqrt(x)+sqrt(y)+1)/(z)`, and `(x+y+z)=k^(2),k in R` then the value of k=

IF lines (x-1)/(2) =(y+1)/(3) =(z-1)/(4) and x-3 =(y-k) /(2) = z intersect then the value of k is

If sqrt(x+1)+sqrt(y)+sqrt(z-4)=(x+y+z)/(2), then find x+y+z

If lines : (x -1)/(2) = (y + 1)/(3) = (z - 1)/(4) and (x - 3)/(1) = (y - k)/(2) = (z)/(1) intersect, then find the value of 'k' and hence find the equation of the plane containing these lines.

If x, y, z are in arithmetic progression with common difference d, x ne 3d , and the determinant of the matrix [(3, 4sqrt(2),x),(4, 5sqrt(2),y), (5, k, z)] is zero, then the value of K^(2) is:

If the lines (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-k)/(2)=(z)/(1) intersect,then find the value of k .

If the lines (x-1)/(k)=(y+1)/(3)=(z-1)/(4)and(x-3)/(1)=(2y-9)/(2k)=(z)/(1) intersect, then find the value of k

If the lines (x-3)/(2)=(y+1)/(3)=(z-2)/(4)and(x-4)/(2)=(y-k)/(2)=(z)/(1) intersect, then find the value of k.

If x:y=2:3 , y:z=3:4 , z:k=1:2 , find the value of x:y:z:k