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.
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