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A vector a has components a(1),a(2) and ...

A vector a has components `a_(1),a_(2) and a_(3)` in a right handed rectangular cartesian system OXYZ. The coordinate system is rotated about Z-axis through angle `(pi)/(2)`. Find components of a in the new system.

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The correct Answer is:
`A_2hati - A_1hatj +A_3hatk`
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 `.
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