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
    If \[A\,(-1,\,\,2,\,\,3),\,\,B\,(1,\,\,1,\,\,1)\] and \[C\,(2,\,\,-1,\,\,3)\] are points on a plane. A unit normal vector to the plane ABC is                                                 [BIT Ranchi 1988]

    A)                 \[\pm \,\left( \frac{2\mathbf{i}+2\mathbf{j}+\mathbf{k}}{3} \right)\]          

    B)                 \[\pm \,\left( \frac{2\mathbf{i}-2\mathbf{j}+\mathbf{k}}{3} \right)\]

    C)                 \[\pm \,\left( \frac{2\mathbf{i}-2\mathbf{j}-\mathbf{k}}{3} \right)\]              

    D)                 \[-\,\left( \frac{2\mathbf{i}+2\mathbf{j}+\mathbf{k}}{3} \right)\]

    Correct Answer: A

    Solution :

               \[\overrightarrow{AB}=2\mathbf{i}-\mathbf{j}-2\mathbf{k},\] \[\overrightarrow{AC}=3\mathbf{i}-3\mathbf{j}+0\mathbf{k}\]                    \[\overrightarrow{AB}\times \overrightarrow{AC}=\left| \begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    2 & -1 & -2  \\    3 & -3 & 0  \\ \end{matrix} \right|=(-6\mathbf{i}-6\mathbf{j}-3\mathbf{k})\]                                 Hence unit vector \[=\pm \left( \frac{2\mathbf{i}+2\mathbf{j}+\mathbf{k}}{3} \right)\,.\]


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