JEE Main & Advanced Mathematics Vector Algebra Question Bank Scaler or Dot product of two vectors and its application

  • question_answer
    If a has magnitude 5 and points north-east and vector b has magnitude 5 and points north-west, then \[|\,\,\mathbf{a}-\mathbf{b}\,\,|\,=\]                                     [MNR 1984]

    A)             25

    B)             5         

    C)             \[7\sqrt{3}\]

    D)             \[5\sqrt{2}\]

    Correct Answer: D

    Solution :

               Since \[\mathbf{a}\,\bot \,\mathbf{b}\Rightarrow \mathbf{a}\,.\,\mathbf{b}=0\]                    \[|\mathbf{a}-\mathbf{b}{{|}^{2}}={{(\mathbf{a}-\mathbf{b})}^{2}}={{a}^{2}}+{{b}^{2}}-2\mathbf{a}\,.\,\mathbf{b}=25+25\]                                 \[\Rightarrow \,\,|\mathbf{a}-\mathbf{b}|\,\,=5\sqrt{2}.\]


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