If `x > 0, y > 0, z>0` and `x^2.y^3.z^4 = 512`, then the least value of `2x + 3y + 4z` is equal to

If ax+13y+bz+c=0 is a plane through the line intersection of 2x+3y-z+1=0, x+y-2z+3=0 and is perpendicular to the plane 3x-y-2z=4 , then the value of 2a+3b+4c is equal to

The plane x + 3y + 13 = 0 passes through the line of intersection of the planes 2x - 8y + 4z = p and 3x - 5y + 4z + 10 =0 . If the plane is perpendicular to the plane 3x - y - 2z - 4 = 0 , then the value of p is equal to

The plane x + 3y + 13 = 0 passes through the line of intersection of the planes 2x - 8y + 4z = p and 3x - 5y + 4z + 10 = 0 If the plane is perpendicular to the plane , 3x - y - 2z - 4 = 0 then the value of p is equal to

If x^(2) + 3y^(2) + 4z^(2)+ 19 = 4 sqrt(3) ( x + y + z) , then the value of ( x - y + 4z) is:

If the plane 2x-y+2z+3=0 has the distances (1)/(3) and (2)/(3) units from the planes 4x-2y+4z+lambda=0 and 2x-y+2z+mu=0 , respectively, then the maximum value of lambda+mu is equal to

If the plane 2x-y+2z+3=0 has the distances (1)/(3) and (2)/(3) units from the planes 4x-2y+4z+lambda=0 and 2x-y+2z+mu=0 , respectively, then the maximum value of lambda+mu is equal to

If the system of equation 14x-3y+z=12, x-2y=0 and x+2z=0 has a solution (x_(0), y_(0), z_(0)) , then the value of x_(0)^(2)+y_(2)^(2)+z_(2)^(2) is equal to

If the system of equation 14x-3y+z=12, x-2y=0 and x+2z=0 has a solution (x_(0), y_(0), z_(0)) , then the value of x_(0)^(2)+y_(2)^(2)+z_(2)^(2) is equal to