A vector `a` has components ` a_1,a_2,a_3` in a right handed rectangular cartesian coordinate system `OXYZ` the coordinate axis is rotated about `z` axis through an angle `pi/2`. The components of `a` in the new system

A vector has component A_(1),A_(2) and A_(3) in a right -handed rectangular Cartesian coordinate system OXY Z .The coordinate system is rotated about the x-axis through an angel pi/2. Find the component of A in the new coordinate system in terms of A_(1),A_(2), and A_(3).

A vector A has components A_(1),A_(2),A_(3) in a right - handed rectangular Cartesian coordinate system Ox,Oy,Oz .The coordinate system is rotated about the z-axis through an angle ((pi)/(2)) .The components of A in the new coordinate system are

If the axes are rotated through an angle 30^(@), the coordinates of (2sqrt(3),-3) in the new system are

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.

The co-ordinates of a point P referred to a rectangular co-ordinate system where O is the origin are (1,-2). The axes are rotated about O through an angle theta. If the co-ordinates of P in the new system are (k-1,k+1), then k^(2) is equal