A horizontal plane `4x-3y+7z=0` is given. Find a line of greatest slope passes through the point `(2,1,1)` in the plane `2x+y-5z=0.`

The staight line passing through the point (1,0,-2) and perpendicular to the plane x-2y+5z-7=0 is

Find the equation of the plane passing through the points (-1,1,1) and (1,-1,1) and perpendicular to the plane x+2y+2z=5.

Find the equation of a plane which passes through the point (3, 2, 0) and contains the line (x-3)/1=(y-6)/5=(z-4)/4

Find ten equation of the plane passing through the point (0,7,-7) and containing the line (x+1)/(-3)=(y-3)/2=(z+2)/1 .

the mirror image of point (3,1,7) with respect to the plane x-y+z=3 is P . then equation plane which is passes through the point P and contains the line x/1=y/2=z/1 .

Find the coordinates of the point where the line through (3,-4,-5) and (2,-3,1) crosses the plane 2x+y+z=7.

Find the distance of the point (2, 3, -2) from the point of intersection of the straight line passing through the points A(3, 0, 1) and B(6, 4, 3) with the plane x+y-z=7 .

Find the non-parametric form of vector equation and Cartesian equation of the plane passing through the point (1,-2,4) and perpendicular to the plane x + 2y - 3z = 11 and parallel to the line (x+7)/(3)=(y+3)/(-1)=(z)/(1).