JEE Main & Advanced Physics Vectors Question Bank Assertion and Reason

  • question_answer
    Assertion             :               If \[\vec{A}.\vec{B}=\vec{B}.\vec{C},\]then \[\vec{A}\] may not always be equal to \[\vec{C}\]                 Reason                 :               The dot product of two vectors involves cosine of the angle between the two vectors.

    A)                 If both assertion and reason are true and the reason is the correct explanation of the assertion.

    B)                 If both assertion and reason are true but reason is not the correct explanation of the assertion.

    C)                 If assertion is true but reason is false.

    D)                 If the assertion and reason both are false.

    E)                 If assertion is false but reason is true.

    Correct Answer: A , C

    Solution :

                        \[\vec{A}.\vec{B}=\vec{B}.\vec{C}\] Þ \[AB\cos {{\theta }_{1}}=BC\cos {{\theta }_{2}}\]                 \ A = C, only when \[{{\theta }_{1}}={{\theta }_{2}}\]                 So when angle between \[\vec{A}\]and \[\vec{B}\] is equal to angle between \[\vec{B}\] and \[\vec{C}\] only then \[\vec{A}\] equal to \[\vec{C}\]

    Solution :

                        Since vector addition is commutative, therefore \[\vec{A}+\vec{B}=\vec{B}+\vec{A}.\]


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