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

  • question_answer
     A unit vector which is perpendicular to \[\mathbf{i}+2\mathbf{j}-2\mathbf{k}\] and \[-\mathbf{i}+2\mathbf{j}+2\mathbf{k}\] is                                 [MP PET 1992]

    A)                 \[\frac{1}{\sqrt{5}}\,(2\mathbf{i}-\mathbf{k})\]              

    B)                 \[\frac{1}{\sqrt{5}}\,(-2\mathbf{i}+\mathbf{k})\]

    C)                 \[\frac{1}{\sqrt{5}}\,(2\mathbf{i}+\mathbf{j}+\mathbf{k})\]       

    D)                 \[\frac{1}{\sqrt{5}}\,(2\mathbf{i}+\mathbf{k})\]

    Correct Answer: D

    Solution :

                    Unit vector is equal to \[\frac{\mathbf{a}\times \mathbf{b}}{|\mathbf{a}\times \mathbf{b}|}=\frac{1}{\sqrt{5}}(2\mathbf{i}+\mathbf{k}).\]


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