Are the points (2,1) and `(-3,5)` on the same or opposite side of the line `3x - 2y + 1 = 0 `?

The equation of the line joining the point {3, 5) to the point of intersection of the lines 4x + y - 1 = 0 and 7x - 3y - 35 = 0 is equidistant from the points (0,0) and (8,34) .

Find the equation of the straight line passing through the point (2,1) and through the point of intersection of the lines x+2y = 3 and 2x-3y=4

The equation of the line through the intersection of the lines 2x - 3y=0 and 4x -5y =2 and {:("Column - I","Column - II"),("(i) through the point (2, 1) is","(a)" (2x - y =4)),("(ii) perpendicular to the line" x + 2y + 1 =0 "is" , "(b)" x+y -5 =0),("(iii) parallel to the line" 3x - 4y + 5=0 "is","(c)" x-y -1 =0),("(iv) equally inclined to the axis is","(d)" 3x-4y-1 =0):}

The line joining the pionts (1,1,2) and (3,-2,1) meets the plane 3x + 2y + z = 6 in ............. Point.

Find the equations of the lines through the point of intersection of the lines x - y + 1 = 0 and 2x - 3y + 5 =0 and whose distance from the point (3,2) is (7)/(5) .

Two oppositive verticies of rectangle are (-3,1) and (1,1) . Also equation of one side is along the line 4x+7y + 5=0 . Find equation of other sides of rectangle.

The equation of the plane passing through the points (-1,1,0) and (2,3,2) and parallel to the line (x-2)/(3) = (y-1)/(1) = (z-1)/(-2) is ..........

Prove that The lines joining the origin to the points of intersection of the line 3x-2y =1 and the curve 3x^2 + 5xy -3y^2+2x +3y= 0 , are are at right angles.

Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to the line x-2y = 1.

Find the equation of the plane containing the line of intersection of the plane x + y + z-6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1).