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

  • question_answer
    If \[\overrightarrow{A}=3\mathbf{i}+\mathbf{j}+2\mathbf{k}\] and \[\overrightarrow{B}=2\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] and q is the angle between \[\overrightarrow{A}\] and \[\overrightarrow{B},\] then the value of \[\sin \theta \] is

    A)                 \[\frac{2}{\sqrt{7}}\]

    B)                 \[\sqrt{\frac{2}{7}}\]

    C)                 \[\frac{4}{\sqrt{7}}\]

    D)                 \[\frac{3}{\sqrt{7}}\]

    Correct Answer: A

    Solution :

               \[\cos \theta =\frac{\overrightarrow{A}\,.\,\overrightarrow{B}}{|\overrightarrow{A}|\,|\overrightarrow{B}|}=\frac{6-2+8}{\sqrt{14}\times \sqrt{24}}\]                 \[\cos \theta =\frac{12}{\sqrt{14}\times \sqrt{24}}=\sqrt{\frac{3}{7}}\], \[\therefore \,\,\,\sin \theta =\frac{2}{\sqrt{7}}\].


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