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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 25

  • question_answer
    The two vectors \[\vec{A}\] and \[\vec{B}\] are drawn from a common point and \[\overset{\to }{\mathop{C}}\,=\overset{\to }{\mathop{A}}\,+\overset{\to }{\mathop{B}}\,\] . Regarding the angle between \[\overset{\to }{\mathop{A}}\,\] and \[\overset{\to }{\mathop{B}}\,\],study the following statements,
    (i) \[90{}^\circ \]if\[{{C}^{2}}={{A}^{2}}+{{B}^{2}}\]                                  
    (ii) greater than \[90{}^\circ \] if \[{{C}^{2}}<{{A}^{2}}+{{B}^{2}}\]
    (iii) greater than \[90{}^\circ \] if \[{{C}^{2}}>{{A}^{2}}+{{B}^{2}}\]
    (iv) less than \[90{}^\circ \]if \[{{C}^{2}}>{{A}^{2}}+{{B}^{2}}\]
    The correct statements are

    A) (i), (ii) and (iii)               

    B) (i), (ii) and (iv)    

    C)      (iii) and (iv)         

    D)        (ii) and (iii)

    Correct Answer: B

    Solution :

    [b] From the addition of two vectors, we know that \[{{C}^{2}}={{A}^{2}}+{{B}^{2}}+2AB\,\,\cos \theta \] From this expression, it is clear that             \[{{C}^{2}}={{A}^{2}}+{{B}^{2}}\] when  \[\theta =90{}^\circ \]             \[{{C}^{2}}<{{A}^{2}}+{{B}^{2}}\] when \[\theta >90{}^\circ \] and       \[{{C}^{2}}>{{A}^{2}}+{{B}^{2}}\] when \[\theta <90{}^\circ \]


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