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JEE Main & Advanced Physics Vectors Question Bank Critical Thinking

  • question_answer
    If a vector \[\overrightarrow{P}\] making angles a, b, and g respectively with the X, Y and Z axes respectively.             Then \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma =\]

    A)                                                                      0     

    B)             1

    C)             2     

    D)              3

    Correct Answer: C

    Solution :

                         \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +\sin \gamma \] \[=1-{{\cos }^{2}}\alpha +1-{{\cos }^{2}}\beta +1-{{\cos }^{2}}\gamma \]             \[=3-({{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma )\]\[=3-1=2\]


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