Find the vector equation of the plane through the point (2,0,-1) and perpendicular to the line joining the two pints (1,2,3) and (3,-1,6).

Find the equation of the plane passing through the points (1,2,1) and perpendicular to the line joining the points (1,4,2) and (2,3,5), Also, find the perpendicular distance of the plane from the origin.

Find the equation of the plane passing through the point (3,-3, 1) and perpendicular to the line joining the points (3, 4, - 1) and (2, - 1,5). Also find the coordinates of the foot of the perpendicular, the equation of the perpendicular line and the length of perpendicular drawn from the origin to the plane.

Find the equation of the plane passing through the point A(1, 2, 1) and perpendicular to the line joining the points P(1, 4, 2) and Q(2, 3, 5). Also, find the distance of this plane from the line (x+3)/(2)=(y-5)/(-1)=(z-7)/(-1)

Find the vector and cartesian equation of a line through the point (1, – 1, 1) and perpendicular to the lines joining the points (4, 3, 2), (1, -1,0) and (1, 2,-1), (2, 1, 1).

Find the vector equation for the line through the points A(3,4,-7) and B(1,-1,6).

Find the vector equation for the line through the points : (1,2,2) and (6,4,6) .

Find the vector equations of the line passing through the point (1,-1,2) and perpendicular to the plane 2x-y+3z-5=0.

Find the vector equation of the plane through the points (2,1,-1) and (-1,3,4) and perpendicular to the plane x-2y+4z=10 .

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

Find the vector equation of the line through the point (2,-1,-1) and is parallel to the line 6x-2=3y+1=2z-2 .