The axes of coordinates are rotated about the z-axis through an angle of `pi//4` in the anticlockwise direction and the components of a vector are `2sqrt2, 3sqrt2, 4`. Prove that the components of the same vector in the original system are `-1, 5, 4`.

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

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

If the axes are rotated through an angle of 30^@ in the anti clockwise direction, then coordinates of point (4,-2sqrt3) with respect to new axes are

A vector sqrt(3)hati + hatj rotates about its tail through an angle 30^(@) in clock wise direction then the new vector is

When a right handed rectangular Cartesian system OXYZ is rotated about the z-axis through an angle pi/4 in the counter-clockwise, direction it is found that a vector veca has the component 2sqrt(3), 3sqrt(2) and 4.

If the axes be turned through an angle tan^-1 2 (in anticlockwise direction), what does the equatio 4xy-3x^2=a^2 become ?

The x and y components of a vector are 4sqrt3 m and 4 m respectively. What angle does the vector make with positive x-axis ?

The axes are rotated through an angle pi//3 in the anticlockwise direction with respect to (0,0) . Find the coordinates of point (4,2) (w.r.t. old coordinate system) in the new coordinates system.

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 represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is