Rotation of a Vector About an Axis
Category : JEE Main & Advanced
Let \[\mathbf{a}=({{a}_{1}},\,{{a}_{2}},\,{{a}_{3}})\]. If system is rotated about
(i) x-axis through an angle \[\alpha \], then the new components of \[\mathbf{a}\] are \[({{a}_{1}},\,{{a}_{2}}\cos \alpha +{{a}_{3}}\sin \alpha ,\,-{{a}_{2}}\sin \alpha +{{a}_{3}}\cos \alpha )\].
(ii) y-axis through an angle \[\alpha \], then the new components of \[\mathbf{a}\] are \[(-{{a}_{3}}\sin \alpha +{{a}_{1}}\cos \alpha ,\,{{a}_{2}},\,{{a}_{3}}\cos \alpha +{{a}_{1}}\sin \alpha )\].
(iii) z-axis through an angle \[\alpha \], then the new components of \[\mathbf{a}\] are \[({{a}_{1}}\cos \alpha +{{a}_{2}}\sin \alpha ,\,-{{a}_{1}}\sin \alpha +{{a}_{2}}\cos \alpha ,{{a}_{3}})\].
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