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

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 :

Write down a unit vector in XY-plane, making an angle of 30^o with the positive direction of x-axis.

Find the slope of the line, which makes an angle of 30^@ with the positive direction of y-axis measured anticlockwise.

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

Find the slope of the line, which makes an angle of 30^@ with the positive direction of y-axis, measured anticlockwise.

If the equation of the pair of straight lines passing through the point (1,1) , one making an angle theta with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x^2-(a+2)x y+y^2+a(x+y-1)=0,a!=2, then the value of sin2theta is

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].