2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-37

  • question_answer
    Given\[\overrightarrow{A}=2\widehat{i}+3\widehat{j}+6\widehat{k},\,\,\overrightarrow{B}=\widehat{i}+\widehat{j}-2\widehat{k}\]and\[\overrightarrow{C}=\widehat{i}+2\widehat{j}+\widehat{k}\]. Compute the value of\[|\overrightarrow{A}\times [\overrightarrow{A}\times (\overrightarrow{A}\times \overrightarrow{B}).\overrightarrow{C}]\].

    A) \[343\]                         

    B) \[512\]

    C) \[221\]                         

    D) \[243\]

    Correct Answer: A

    Solution :

    \[\overrightarrow{V}=\overrightarrow{A}\times \left[ (\overrightarrow{A}.\overrightarrow{B})\overrightarrow{A}-(\overrightarrow{A}.\overrightarrow{A})\overrightarrow{B} \right].\overrightarrow{C}\] \[=\left( \underbrace{\overrightarrow{A}\times (\overrightarrow{A}.\overrightarrow{B})\overrightarrow{A}}_{zero}-(\overrightarrow{A}.\overrightarrow{A})\overrightarrow{A}\times \overrightarrow{B} \right).\overrightarrow{C}=-|\overrightarrow{A}{{|}^{2}}[\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}]\]Now,\[|\overrightarrow{A}{{|}^{2}}=4+9+36=49\] \[[\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}]=\left| \begin{matrix}    2 & 3 & 6  \\    1 & 1 & -2  \\    1 & 2 & 1  \\ \end{matrix} \right|\]             \[=2(1+4)-1(3+12)+1(-6+6)\]             \[=10+9-12=7\] \[\therefore \]    \[\left| -|\overrightarrow{A}{{|}^{2}}[\overrightarrow{A}\overrightarrow{B}\overrightarrow{C}] \right|=49\times 7=343\]


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