A) (1, 5, 1)
B) (1, 3, 1)
C) \[\left( -\frac{1}{2},\,\,4,\,\,0 \right)\]
D) \[\left( \frac{1}{2},\,\,4,\,\,-2 \right)\]
Correct Answer: C
Solution :
\[\overrightarrow{a}.\overrightarrow{c}=0\,\,\Rightarrow \,\,6+6\lambda +3({{\lambda }_{3}}-1)=0\] \[\Rightarrow \,\,{{\lambda }_{3}}\,=\,-2{{\lambda }_{1}}-1\] \[\overrightarrow{b}=2\overrightarrow{a}\,\,\Rightarrow \,\,3-{{\lambda }_{2}}=2{{\lambda }_{1}}\] \[\Rightarrow \,\,{{\lambda }_{2}}=3-2{{\lambda }_{1}}\] \[Let\,\,\,{{\lambda }_{1}}=1;\,\,{{\lambda }_{2}}=1;\text{ }{{\lambda }_{3}}=-3\] \[{{\lambda }_{1}}=-\frac{1}{2};\,\,{{\lambda }_{2}}=4;\text{ }{{\lambda }_{3}}=0\] \[{{\lambda }_{1}}=\frac{1}{2};\,\,{{\lambda }_{2}}=2;\text{ }{{\lambda }_{3}}=-2\]You need to login to perform this action.
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