A) \[{{\lambda }_{1}}=7\]
B) \[{{\lambda }_{1}}+{{\lambda }_{3}}=3\]
C) \[{{\lambda }_{1}}+{{\lambda }_{2}}+{{\lambda }_{3}}=3\]
D) None of these
Correct Answer: D
Solution :
| \[2\vec{a}-3\vec{b}+4\vec{c}\] |
| \[=({{\lambda }_{1}}-{{\lambda }_{2}}+{{\lambda }_{3}})\,\,\vec{a}+(-\,{{\lambda }_{1}}+{{\lambda }_{2}}-{{\lambda }_{3}})\,\,\vec{b}+({{\lambda }_{1}}+{{\lambda }_{2}}+{{\lambda }_{3}})\,\,\vec{c}\]Now \[{{\lambda }_{1}}-{{\lambda }_{2}}+{{\lambda }_{3}}=2,\] |
| \[-\,{{\lambda }_{1}}+{{\lambda }_{2}}-\,{{\lambda }_{3}}=-\,3\] \[\Rightarrow {{\lambda }_{1}}-{{\lambda }_{2}}+{{\lambda }_{3}}=3\] |
| Clearly, these two condition can?t be true together |
| So \[\lambda \in \phi \] |
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