Fill in the blanks:
The equation of the line passing thorugh (5,2) and perpendicular to the lines joining the points (2,3) and (3,-1) is …………..

The equation of the line passing through (1,2) and perpendicular to the line x+y+1=0 is :

Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).

Find the equation of a line passing through (4,5) and perpendicular to the line 2x + 3y=5.

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 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).

Fill in the blanks : The equation of the line passing through (1, 2, 3) and parallel to 3hati-hatj+2hatk is ……… .

Find the equation of the line through point (5,-2) and perpendicular to line 2x+3y-7=0.