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

JEE Main & Advanced Mathematics Vector Algebra Question Bank Self Evaluation Test - Vector Algebra

  • question_answer
    If the vectors \[\alpha \hat{i}+\alpha \hat{j}+\gamma \hat{k},\text{ }\hat{i}+\hat{k}\] and \[\gamma \hat{i}+\gamma \hat{j}+\beta \hat{k}\] lie on a plane, where \[\alpha ,\beta \] and \[\gamma \] are distinct non-negative numbers, then \[\gamma \] is

    A) Arithmetic mean of \[\alpha \] and \[\beta \]

    B) Geometric mean of \[\alpha \] and \[\beta \]

    C) Harmonic mean of \[\alpha \] and \[\beta \]

    D) None of the above

    Correct Answer: B

    Solution :

    [b] If three vectors are co-planar. \[\Rightarrow \left| \begin{matrix}    \alpha  & \alpha  & \gamma   \\    1 & 0 & 1  \\    \gamma  & \gamma  & \beta   \\ \end{matrix} \right|=0\] \[\Rightarrow \alpha [0-\gamma ]-\alpha [\beta +\gamma ]+\gamma [\gamma -0]=0\] \[\Rightarrow -\alpha \gamma -\alpha \beta +\alpha \gamma +{{\gamma }^{2}}=0\] \[\Rightarrow {{\gamma }^{2}}=\alpha \beta \] \[\Rightarrow \]   So \[\alpha ,\beta ,\gamma \] are in G.P.


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