JEE Mains · Physics · STD 11 - 3.1 vectors
Let \(\vec A\, = \,(\hat i\, + \,\hat j)\,\) and \(\vec B\, = \,(2\hat i\, - \,\hat j)\,.\) The magnitude of a coplanar vector \(\vec C\) such that \(\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B\) is given by
- A \(\sqrt {\frac{5}{9}} \)
- B \(\sqrt {\frac{10}{9}} \)
- C \(\sqrt {\frac{20}{9}} \)
- D \(\sqrt {\frac{9}{12}} \)
Answer & Solution
Correct Answer
(A) \(\sqrt {\frac{5}{9}} \)
Step-by-step Solution
Detailed explanation
\begin{array}{l} If\,\vec C = a\hat i + b\hat j\,then\,\vec A.\vec C = \vec A.\vec B\\ a + b = 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\ \vec B.\vec C = \vec A.\vec B\\ 2a - b =…
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