A st. line is drawn through the point `P(sqrt3 ,2)` making an angle of `pi/6` with positive direction of the x-axis. If meets the st. line `sqrt3x-4y+8=0` in Q, find the length of [PQ].

Find the inclination to the x-axis of the lines : sqrt3 x-y +2=0 .

Find the equation of a line through the origin, which makes an angle of 45^@ with the positive direction of x-axis.

Find the equation of a st. line, which passes through the point (-2,3) and makes an angle of 60^@ with the positive direction of x-axis.

Find slope of the line that makes angle (2pi)/3 with the positive direction of x-axis.

A line passing through the point (3, 0) makes an angle 30^@ with the positive direction of x-axis. If this line is rotated through an angie of 15^@ in clockwise direction, find its equation in new position.

Find the equation of the lines through the point (3,2) which make an angle of 45^@ with the line x-2y=3.

If a line makes an angle of pi/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of z-axis is

A line through the point A (2, 0), which makes an angle of 30^@ with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15^@ . Then the equation of the straight line in the new position is :

Find equation of the line through the point (0, 2) making an angle (2pi)/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.