Angle of a line with the positive direction of the x-axis is `theta` . The line is rotated about some point on it in anticlockwise direction by angle `45^0` and its slope becomes `3.` Find the angle `thetadot`

A line through the point P (1, 2) makes an angle of 60^0 with the positive direction of x-axis and is rotated about P in the clockwise direction through an angle 15^0 . Find the equation of the straight line in the new position.

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

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

A line segement AB through the point A(2, 0) which makes an angle of 30^0 with the positive direction of x-axis is rotated about A in anticlockwise direction through an angle of 15^0 . If C be the new position of point B(2+sqrt(3) , 1) , find the coordinates of C .

A vector 3i + 4j rotates about its tail through an angle 37° in anticlockwise direction then the new vector is

Find the slope of a line whose inclination to the positive direction of x-axis in anticlockwise sense is (a) 30^(@) (b) 150^(@)

If a line makes angle 90o , 60o and 30o with the positive direction of x, y and z-axis respectively, find its direction cosines.

If a line makes angle 90o , 60o and 30o with the positive direction of x, y and z-axis respectively, find its direction cosines.

A point (1, 1) undergoes reflection in the x-axis and then the coordinates axes are rotated through an angle of pi/4 in anticlockwise direction. The final position of the point in the new coordinate system is