Determine whether the following satis fy the vector trans formation rule (a) \( (x-y, x+y, 0) \), for rotation about the \( z \)-axis (b) \( (0,2 z+y, z-2 y) \) for rotation about \( x \)-axis (c) \( \left(y^{2}+z^{2},-x y,-x z\right) \) for rotations about each of the three coordinate axes?
Added by Sadeem Z.
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The given transformation is \((x-y, x+y, 0)\), which sets the \(z\)-coordinate to 0. This means that it does not satisfy the vector transformation rule for rotation about the \(z\)-axis. Show more…
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