JEE Main & Advanced Mathematics Vector Algebra Question Bank Critical Thinking

  • question_answer
    Three forces of magnitudes 1, 2, 3 dynes meet in a point and act along diagonals of three adjacent faces of a cube. The resultant force is [MNR 1987]

    A) 114 dyne

    B) 6 dyne

    C) 5 dyne

    D) None of these

    Correct Answer: C

    Solution :

    • Three vectors meeting at a point are \[\mathbf{i}+\mathbf{j},\,\mathbf{j}+\mathbf{k},\,\mathbf{k}+\mathbf{i}\]. Forces of 1, 2, 3 dynes are acting along these directions respectively, therefore resultant force                   
    • = \[\frac{\mathbf{i}+\mathbf{j}}{\sqrt{2}}+\frac{2(\mathbf{j}+\mathbf{k})}{\sqrt{2}}+\frac{3(\mathbf{k}+\mathbf{i})}{\sqrt{2}}=\frac{4\mathbf{i}+3\mathbf{j}+5\mathbf{k}}{\sqrt{2}}\],                   
    • \[\therefore \] Magnitute = \[\frac{5\sqrt{2}}{\sqrt{2}}=\]5 dyne.

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