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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    The direction cosines of the resultant of the vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(-\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[(\mathbf{i}-\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+\mathbf{j}-\mathbf{k}),\] are

    A) \[\left( \frac{1}{\sqrt{2}},\,\,\frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{6}} \right)\]

    B) \[\left( \frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}},\,\,\frac{1}{\sqrt{6}} \right)\]

    C) \[\left( -\frac{1}{\sqrt{6}},\,\,-\frac{1}{\sqrt{6}},\,-\,\frac{1}{\sqrt{6}} \right)\]            

    D) \[\left( \frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{3}},\,\frac{1}{\sqrt{3}} \right)\]

    Correct Answer: D

    Solution :

    Resultant vector \[=2\mathbf{i}+2\mathbf{j}+2\mathbf{k}.\] Direction cosines are \[\left( \frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{3}},\,\,\frac{1}{\sqrt{3}} \right)\,.\]


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