Find the value of lambda for which the p...

Find the value of `lambda` for which the plane `x+y+z=sqrt(3)lambda` touches the sphere `x^2+y^2+z^2-2x-2y-2z=6.`

Verified by Experts

The correct Answer is:

`lambda=sqrt(3)pm3`

Similar Questions

Explore conceptually related problems

Show that the plane 2x-2y+z+12=0 touches the sphere x^2+y^2+z^2-2x-4y+2z-3=0.

Find the centre and radius of the sphere 2x^2+2y^2+2z^2-2x+4y+2z+3=0 .

Find the measure of the angle between the planes 2x-y+z=2 and x+y+2z=3

The value of m for which straight line 3x-2y+z+3=0=4x-3y+4z+1 is parallel to the plane 2x-y+mz-2=0 is

The value of lambda for which the system of equations 2x-y-2z=2,x-2y +z = -4, x+y+lamda z=4 has no solution is

The plane x+2y-z=4 cuts the sphere x^(2)+y^(2)+z^(2)-x+z-2=0 in a circle of radius

The values of lambda for which the system of equations x+y+z=6,x+2y+3z=10, x+2y+lambdaz=12 is inconsistent

Find the equation the equation of sphere cocentric with sphere 2x^2+2y^2+2z^2-6x+2y-4z=1 and double its radius.

Find the equation of the image of the plane x-2y+2z-3=0 in plane x+y+z-1=0.

The radius of the circle in which the sphere x^2+y^2+z^2+2x-2y-4z-19=0 is cut by the plane x+2y+2z+7=0 is