Vector A- has components A1-A2-A3 along the three axes If the co-ordinates system is roatated by 90- about z-axis then the new components along the axes are

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Question

Vector $\to A$ has components $A_{1}, A_{2}, A_{3}$ along the three axes If the co-ordinates system is roatated by $90^{\circ}$ about z-axis then the new components along the axes are

A_{1}, - A_{2}, A_{3}

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- A_{1}, - A_{2}, A_{3}

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A_{2}, - A_{1}, A_{3}

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- A_{2}, - A_{1}, A_{3}

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Solution

The correct option is A $A_{2}, - A_{1}, A_{3}$
Facing the z axis, there can be two possibilities. Either, clockwise rotation or anticlockwise rotation.
In case of clockwise rotation we get
$(A_{1} i + A_{2} j + A_{3} k) \to (A_{2} i - A_{1} j + A_{3} k)$
In case of anticlockwise rotation, we get
$A_{1} i + A_{2} j + A_{3} k \to (- A_{2} i + A_{1} j + A_{3} k)$ .

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Vector →A has components A1,A2,A3 along the three axes If the co-ordinates system is roatated by 90∘ about z-axis then the new components along the axes are

The correct option is A A2,−A1,A3Facing the z axis, there can be two possibilities. Either, clockwise rotation or anticlockwise rotation.In case of clockwise rotation we get (A1i+A2j+A3k)→(A2i−A1j+A3k)In case of anticlockwise rotation, we get A1i+A2j+A3k→(−A2i+A1j+A3k).

Vector $\to A$ has components $A_{1}, A_{2}, A_{3}$ along the three axes If the co-ordinates system is roatated by $90^{\circ}$ about z-axis then the new components along the axes are