The plane `a x+b y=0` is rotated through an angle `alpha` about its line of intersection with the plane `z=0.` Show that the equation to the plane in the new position is `ax+ b y+-zsqrt(a^2+b^2)tan alpha=0.`

The plane 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane 5x+3y+10 z=25. The equation of the plane in its new position is x-4y+6z=k where k is

The plane 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane 5x+3y+10 z=25. The equation of the plane in its new position is a. x-4y+6z=106 b. x-8y+13 z=103 c. x-4y+6z=110 d. x-8y+13 z=105

The plane 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane 5x+3y+10 z=25. The equation of the plane in its new position is a. x-4y+6z=106 b. x-8y+13 z=103 c. x-4y+6z=110 d. x-8y+13 z=105

The plane lx + my = 0 is rotated about its line of intersection with the plane z= 0 through an angle alpha . The equation changes to

The x-y plane is rotated about its line of intersection with the y-z plane by 45^0 , then the equation of the new plane is/are a. z+x=0 b. z-y=0 c. x+y+z=0 d. z-x=0

Prove that the equation of the plane which is pendicular to the plane 3x+2y+6z+4=0 is 2x-6y+z=0 .

The equation of the plane through the line of intersection of the planes 2x+y-z+5=0 and x+2y+3z=4 and perpendicular to the plane 5x+3y+6z=10 is -

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x+2y+z=10 at

If the lines represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

Find the intercepts made by the plane x-2y+3z-18=0 on the axes.