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

Answer

`A_2hati - A_1hatj +A_3hatk`

Explanation

Since vector `vecA` has components `A_1, A_2 and A_3`, in the coordinates system OXYZ,
`vecA = hati A_1 + hatj A_2 + hatk A_3`
When given system is rotated through `pi//2`, the new x-axis is along the old y-axis and the new y-axis is along the old negative x-axis, z remains same as before.
Hence, the components of A in the new system are `A_2, -A_1 and A_3`.
Therefore, `vecA` becomes `A_2 hati - A_1 hatj + A_3 hatk `.