2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Determinants & Matrices

JEE Main & Advanced Mathematics Determinants & Matrices Question Bank System of linear equations, Some special determinants, differentiation and integration of determinants

  • question_answer
    If \[a_{i}^{2}+b_{i}^{2}+c_{i}^{2}=1,\,\,(i=1,2,3)\] and \[{{a}_{i}}{{a}_{j}}+{{b}_{i}}{{b}_{j}}+{{c}_{i}}{{c}_{j}}=0\] \[(i\ne j,i,j=1,2,3)\] then the value of \[{{\left| \,\begin{matrix}    {{a}_{1}} & {{a}_{2}} & {{a}_{3}}  \\    {{b}_{1}} & {{b}_{2}} & {{b}_{3}}  \\    {{c}_{1}} & {{c}_{2}} & {{c}_{3}}  \\ \end{matrix}\, \right|}^{2}}\] is [AMU 1994; DCE 2001]

    A) 0

    B) 1/2

    C) 1

    D) 2

    Correct Answer: C

    Solution :

    \[{{\left| \,\begin{matrix}    {{a}_{1}} & {{a}_{2}} & {{a}_{3}}  \\    {{b}_{1}} & {{b}_{2}} & {{b}_{3}}  \\    {{c}_{1}} & {{c}_{2}} & {{c}_{3}}  \\ \end{matrix}\, \right|}^{2}}=\left| \,\begin{matrix}    {{a}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{a}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{a}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix}\, \right|\,\left| \,\begin{matrix}    {{a}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{a}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{a}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix}\, \right|\], \[[\because \,|A|=|{A}'|]\] \[=\left| \,\begin{matrix}    1 & 0 & 0  \\    0 & 1 & 0  \\    0 & 0 & 1  \\ \end{matrix}\, \right|=1\].


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