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.`

Find the equations of the line passing through the point (-4,3,1) perpendicular to the plane x+2y-z=0 .

Find the equation of the plane .Passing through the point (2,3-1) and parallel to the plane 3x-4y+7z=0.

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 4x-2y-5z-2=0.

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 4x-2y-5z-2=0

find the equation of a plane passing through the points (2,-1,0) and (3,-4,5) and parallel to the line 2x=3y=4z

Assuming the plane 4x-3y+7z=0 to be horizontal, the direction cosines of line greatest slope in the plane 2x+y-5z=0 are

(i) Find the equation of the plane passing through (1,-1,2) and perpendicular to the planes : 2 x + 3y - 2z = 5 , x + 2y - 3z = 8 . (ii) find the equation of the plane passing through the point (1,1,-1) and perpendicular to each of the planes : x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0 . (iii) Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to the planes : 3x + 2y - 3z = 1 and 5x - 4y + z = 5.

Find the equations to the line of greatest slope through the point (7,2,-1) in the plane x-2y+3z=0 assuming that the axes are so placed that the plane 2x+3y4z=0 is horizontal

The line of greatest slope on an inclined plane P_1 is that line in the plane which is perpendicular to the line of intersection of plane P_1 and a horiontal plane P_2 . Q. Assuming the plane 4x-3y+7z=0 to be horizontal, the direction cosines of line greatest slope in the plane 2x+y-5z=0 are