2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Vector Algebra

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

  • question_answer
    The perimeter of the triangle whose vertices have the position vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})\] and \[(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),\] is given by                                                                                                              [MP PET 1993]

    A) \[15+\sqrt{157}\]

    B) \[15-\sqrt{157}\]

    C) \[\sqrt{15}-\sqrt{157}\]       

    D) \[\sqrt{15}+\sqrt{157}\]

    Correct Answer: A

    Solution :

    \[\mathbf{a}=4\mathbf{i}+2\mathbf{j}-4\mathbf{k}\Rightarrow \,\,|\mathbf{a}|\,\,=\sqrt{16+16+4}=6\] \[\mathbf{b}=-3\mathbf{i}+2\mathbf{j}+12\mathbf{k}\Rightarrow \,\,|\mathbf{b}|\,\,=\,\,\sqrt{144+4+9}=\sqrt{157}\] \[\mathbf{c}=-\mathbf{i}-4\mathbf{j}-8\mathbf{k}\Rightarrow \,\,|\mathbf{c}|\,\,=\,\,\sqrt{64+16+1}=9\] Hence perimeter is \[15+\sqrt{157}.\]   


You need to login to perform this action.
You will be redirected in 3 sec spinner