[" angle of "30^(@)" with positive direction of the "x" -axis "],[" Passing through the points "(-1,1)" and "(2,-4).]

Find the equation of a line making an angle 2pi//3 with positive direction of x-axis and passing through a point (0,2) .

Find the equation of a line (i) whose slope is 4 and which passes through the point (5, -7), (ii) whose slope is -3 and which passes through the point (-2, 3), (iii) which makes an angle of ((2pi)/(3)) with the positive direction of the x-axis and passes through the point (0, 2).

A line makes an acute angle with the positive direction of x-axis and passes through the points (6, -7, -1) and (2, -3, 1), find the direction cosines of the line.

(i) Find the equation of line passing through (2,2) and makes an angle of 135^(@) from positive direction of X -axis. (ii) Find the equation of a line passing through the point (2,1) and makes an angle 'theta' from the positive direction of X -axis where cos theta=-(1)/(3) .

A straight line passing through (1, 1, 1) makes an angle of 60^(@) with the positive direction of the z-axis, and the cosines of the angles made with the positive directions of y, x-axis are in the ratio sqrt(3):1 . Then the acute angle between the two possible positions of the line is

A straight line passing through A (-2,1) , makes an angle of 30^(@) with the positive direction of the X-axis. Find the points on the straight line whose distance from A is 4 units.

A straight line passes throught the point (-1,4) and makes an angle 60^(@) with the positive direction of the x- axis . Find the equation of the straight line.

A line throught 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^(@) . The eqation of the straight line in the new position is -