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 straight line passing through the point (3,2) and perpendicular to the line y=x is,

The equation of the line passing through (1, 1, 1) and perpendicular to the line of intersection of the planes x+2y-4z=0 and 2x-y+2z=0 is

Find the equation of the line parallel to Y -axis and drawn through the point of intersection of the lines x-7y + 5=0 and 3x +y=0 .

Find the vector equation for the line passing through the points (-1, 0, 2) and (3, 4, 6).

Find the combined equation of the straight lines passing through the point (1,1) and parallel to the lines represented by the equation . x^2-5xy+4y^2+x+2y-2=0 .

Find the equation of the line passing through the point (5, 2) and perpendicular to the line segment joining the points (2, 3) and (3, -1).

Find the direction in which a straight line must be drawn through the point (-1,2) . So that its point of intersection with the line x+y=4 may be at a distance of 3 units from this point.