The plane `2x-2y+z=3` is rotated about its line of intersection with the `xy` -plane by an acute angle `alpha` .If the new position of the plane contains the point `(3,1,1)` ,then the value of `cos alpha` is equal to

The plane x-y-z=4 is rotated through 90^(@) about tits line of intersection with the plane x+y+2z=4. Find its equation in the new position,

If the plane x+y+z=1 is rotated through 90^(@) about its line of intersection with the plane x-2y+3z=0, the new position of the plane is

The plane x-y-z=4 is rotated through an angle 90^(@) about its line of intersection with the plane x+y+2z=4 . Then the equation of the plane in its new position is

The plane x+2y+3z=7 is rotated about the line where it cut y z -plane by an angle theta . In the new position the plane contains the point (-1,0,2)dot Then theta a.cos^(-1)1/7 b. cos^(-1)6/7 c. cos^(-1)(5/7) d. pi/2

The plane x-2y+3z=0 is rotated through a right angle about the line of intersection with the plane 2x+3y-4z-5=0, find the equation of the plane in its new position.

The plane x- y - z = 2 is rotated through an angle pi/2 about its line of intersection with the plane x + 2y + z = 2 . Find its equation in the new position.

The plane x-y-z=2 is rotated through 90^(@) about its line of intersection with the plane x+2y+z=2 . The distance of (-1,-2,-1) from the plane in the new position is lamda sqrt(6/7) . Then the value of lamda is equal to

The plane ax+by=0 is rotated about its line of intersection with the plane z=0 through an angle alpha. Prove that the equation of the plane in its new position is ax+by+-(sqrt(a^(2)+b^(2))tan alpha)z=0