AP EAMCET · Maths · Vector Algebra
\(\bar{a}, \bar{b}, \bar{c}\) are three vectors such that \(|\bar{a}|=2,|\bar{b}|=3,|\bar{c}|=5,|\bar{a}+\bar{b}+\bar{c}|=\sqrt{69}\). If \((\bar{a}, \bar{b})=(\bar{b}, \bar{c})=\frac{\pi}{3}\) then \((\bar{c}, \bar{a})=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(|\bar{a}+\bar{b}+\bar{c}|^2 = |\bar{a}|^2 + |\bar{b}|^2 + |\bar{c}|^2 + 2(\bar{a} \cdot \bar{b} + \bar{b} \cdot \bar{c} + \bar{c} \cdot \bar{a})\) \(69 = 2^2 + 3^2 + 5^2 + 2(2 \cdot 3 \cos(\frac{\pi}{3}) + 3 \cdot 5 \cos(\frac{\pi}{3}) + 5 \cdot 2 \cos((\bar{c}, \bar{a})))\)…
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