Solve this following

Question:

Let $\overrightarrow{\mathrm{A}}=(\hat{\mathrm{i}}+\hat{\mathrm{j}})$ and $\overrightarrow{\mathrm{B}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}})$. The magnitude of a coplanar vector $\overrightarrow{\mathrm{C}}$ such that $\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}$,

is given by :-

  1. $\sqrt{\frac{20}{9}}$

  2. $\sqrt{\frac{5}{9}}$

  3. $\sqrt{\frac{9}{12}}$

  4. $\sqrt{\frac{10}{9}}$


Correct Option: , 2

Solution:

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