JEE Mains · Physics · STD 11 - 3.1 vectors
If \(\vec{a}\) and \(\vec{b}\) makes an angle \(\cos ^{-1}\left(\frac{5}{9}\right)\) with each other, then \(|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|\) for \(|\vec{a}|=n|\vec{b}|\) The integer value of \(n\) is _______.
- A \(3\)
- B \(5\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(\cos \theta=\frac{5}{9}\) \(\frac{\vec{a} \cdot \vec{b}}{a b}=\frac{5}{9}\) \(\mid \vec{a}+\cdots(1)\) \(a^2+b^2+2 \vec{a} \cdot \vec{b}=2 a^2+2 b^2-4 \vec{a} \cdot \vec{b}\) \(6 \vec{a} \cdot \vec{b}=a^2+b^2\) \(6 \times \frac{5}{9} a b=a^2+b^2\)…
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