A) \[\left( \frac{4}{3},0 \right)\]
B) \[\left( -\frac{4}{3},0 \right)\]
C) \[\left( \frac{3}{4},0 \right)\]
D) \[\left( -\frac{3}{4},0 \right)\]
Correct Answer: B
Solution :
We know that \[cso\,\theta =\frac{\vec{a}\,.\vec{b}}{|\vec{a}|\,|\vec{b}|}\] \[=\frac{c{{({{\log }_{2}}x)}^{2}}-12+6c\,{{\log }_{2}}x}{\left[ \begin{align} & \sqrt{{{(c\,{{\log }_{2}}x)}^{2}}+36+9} \\ & \times \sqrt{{{({{\log }_{2}}x)}^{2}}+4+4{{(c\,{{\log }_{2}}x)}^{2}}} \\ \end{align} \right]}\] Since, angle is obtuse \[\therefore \] \[\cos \,\theta <0\] \[\Rightarrow \] \[c{{({{\log }_{2}}x)}^{2}}-12+6c\,{{\log }_{2}}x<0\] \[\Rightarrow \] \[c<0\] and \[D<0\] \[\Rightarrow \] \[c<0\] and \[{{(6c)}^{2}}+48c<0\] \[\Rightarrow \] \[c<0\] and \[c<-\frac{4}{3}\] \[\therefore \] \[c\in \left( -\frac{4}{3},0 \right)\]
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