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

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

  • question_answer
    The position vectors of the points A, B and C are \[\mathbf{i}+\mathbf{j},\,\,\mathbf{j}+\mathbf{k}\] and \[\mathbf{k}+\mathbf{i}\] respectively. The vector area of the \[\Delta ABC=\pm \,\frac{1}{2}\overrightarrow{\alpha }\] where \[\overrightarrow{\alpha }=\] [MP PET 1989]

    A)                 \[-\mathbf{i}+\mathbf{j}+\mathbf{k}\]

    B)                 \[\mathbf{i}-\mathbf{j}+\mathbf{k}\]

    C)                 \[\mathbf{i}+\mathbf{j}-\mathbf{k}\]

    D)                 \[\mathbf{i}+\mathbf{j}+\mathbf{k}\]

    Correct Answer: D

    Solution :

               Vector area \[=\frac{1}{2}(\overrightarrow{AB}\times \overrightarrow{AC})=\frac{1}{2}|(-\mathbf{i}+\mathbf{k})\times (-\mathbf{j}+\mathbf{k})|\]                                     \[=\frac{1}{2}\left| \begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    -1 & 0 & 1  \\    0 & -1 & 1  \\ \end{matrix} \right|=\frac{1}{2}(\mathbf{i}+\mathbf{j}+\mathbf{k})\]                                 Hence by comparing, \[\overrightarrow{\alpha }=\mathbf{i}+\mathbf{j}+\mathbf{k}.\]


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