\[{{\mathbf{r}}_{1}}=\mathbf{a}-\mathbf{b}+\mathbf{c},\,\,{{\mathbf{r}}_{2}}=\mathbf{b}+\mathbf{c}-\mathbf{a},\,\,{{\mathbf{r}}_{3}}=\mathbf{c}+\mathbf{a}+\mathbf{b},\] |
\[\mathbf{r}=2\mathbf{a}-3\mathbf{b}+4\mathbf{c}.\] If \[\mathbf{r}={{\lambda }_{1}}{{\mathbf{r}}_{1}}+{{\lambda }_{2}}{{\mathbf{r}}_{2}}+{{\lambda }_{3}}{{\mathbf{r}}_{3}},\] then |
A) \[{{\lambda }_{1}}=7\]
B) \[{{\lambda }_{1}}+{{\lambda }_{3}}=3\]
C) \[{{\lambda }_{1}}+{{\lambda }_{2}}+{{\lambda }_{3}}=4\]
D) \[{{\lambda }_{3}}+{{\lambda }_{2}}=2\]
Correct Answer: B
Solution :
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