A) \[12\]
B) \[50\]
C) \[5\sqrt{2}\]
D) none of these
Correct Answer: C
Solution :
Key Idea: If\[\cos \alpha ,\,\,\cos \beta \]and\[\cos \gamma \]are the direction cosines of a line, then \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] In\[\Delta \,ABC\], \[\cos \alpha =\frac{3}{AB}\] In\[\Delta \,\,ABD\], \[\cos \beta =\frac{4}{AB}\] And in\[\Delta \,ABE\], \[\cos \gamma =\frac{5}{AB}\] We know, \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] \[\Rightarrow \] \[{{\left( \frac{3}{AB} \right)}^{2}}+{{\left( \frac{4}{AB} \right)}^{2}}+{{\left( \frac{5}{AB} \right)}^{2}}=1\] \[\Rightarrow \] \[A{{B}^{2}}=9+16+25\] \[\Rightarrow \] \[A{{B}^{2}}=50\] \[\Rightarrow \]You need to login to perform this action.
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