A vector `hati+sqrt(3)hatj` rotates about its tail through an angle `60^(@)` in clockwise direction then the new vector is

A vector 4hat i+3hat j rotates about its tail through an angle 53^(@) in anticlockwise direction then the new vector is

The line passing through (7,3),(5,1) meets the x-axis at If the line is rotated through an angle 30^(@) in the anti clockwise direction about P then the slope of its new position is

If the axes are rotated through an angle of 30^(@) in the clockwise direction, the point (4,-2 sqrt3) in the new system was formerly

The point represented by the complex number 2-i is rotated about origin through on angle pi/2 the clockwise direction, the new position of the point 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.

If the axes are rotated through an angle of 45^(@) in the clockwise direction, the coordinates of a point in the new systeme are (0,-2) then its original coordinates are

If the axes are rotated through an angle of 30^(@) in the anti clockwise direction,then coordinates of point (4,-2sqrt(3)) with respect to new axes are

The complex number z=1+i is rotated through an angle (3 pi)/(2) in anti-clockwise direction about the origin and stretched by aditional sqrt(2) unit,then the new complex number 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 of 15^(@) . Then, the equation of the striaght line in the new position is