JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Three Dimensional Geometry

  • question_answer
    If a line in the space makes angle \[\alpha ,\beta \] and \[\gamma \] with the coordinate axes, then \[cos\text{ }2\alpha +cos2\beta \] \[+cos\,2\gamma +{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma \]equals. test- The two given expressions on both the sides of the \['='\] sign will have the same value if two numbers from either side or both sides are interchanged. Select the correct numbers to be interchanged from the given options. \['='\] चिन्‍ह के दोनों ओर दिए गए व्यंजकों का मान तब बराबर होगा जब उनमें किसी एक ओर या दोनों ओर की संख्याओं को आपस में बदला जाएगा। दिए गए विकल्पों में से आपस में बदली जाने वाली सही संख्याओं का चयन करें। \[3+5\times 4-24\div 3=7\times 4-3+36\div 6\]

    A) -1

    B) 0

    C) 1

    D) 2

    Correct Answer: C

    Solution :

    [c] \[\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{{\sin }^{2}}\alpha \]                         \[+{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma \] \[={{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\]


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