Prove that through a given point, we can draw only perpendicular to a given line.

Prove that, through three given points which are not collinear, there is only one circle.

The equation of straight line passing through the point (2, 3) and perpendicular to the line 4x -3y = 10 is:

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.

A line passes through the point (2,2) and is perpendicular to the line 3x + y =3, then its y -intercept is

Prove that there is only one triple point.

Find the vector and cartesian equations of the plane which passes through the point (5,2,-4) and perpendicular to the line with direction ratios ,

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

A line passes through point (2, 2) and perpendicular to the line 3x + y = 3. Then y - intercept is :

Given a line and a point, not on the line, there is one and only ........... line which passes through the given point and is .......to the given line.

Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.