A) \[\sqrt{\frac{5}{9}}\]
B) \[\sqrt{\frac{10}{9}}\]
C) \[\sqrt{\frac{20}{9}}\]
D) \[\sqrt{\frac{9}{12}}\]
Correct Answer: A
Solution :
[a] Let the vector \[\vec{C}\]be\[x\hat{i}+y\hat{j}\] |
\[\vec{A}.\vec{C}=x+y=1\] |
and \[\vec{B}.\vec{C}=2x-y=1\] |
Solving these two equations simultaneously |
\[x=2/3\]and \[y=1/3\] |
Hence \[|\vec{C}|=\sqrt{\frac{4}{9}+\frac{1}{9}}=\sqrt{\frac{5}{9}}\] |
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