TS EAMCET · Maths · Vector Algebra
\(\vec{a}, \vec{b}, \vec{c}\) are three vectors each having \(\sqrt{2}\) magnitude such that \((\vec{a}, \vec{b})=(\vec{b}, \vec{c})=(\vec{c}, \vec{a})=\frac{\pi}{3}\). If \(\vec{x}=\vec{a} \times(\vec{b} \times \vec{c})\) and \(\vec{y}=\vec{b} \times(\vec{c} \times \vec{a})\), then
- A \(|\vec{x}|=|\vec{y}|\)
- B \(|\vec{x}|=\sqrt{2}|\vec{y}|\)
- C \(|\vec{x}|=2|\vec{y}|\)
- D \(|\vec{x}|+|\vec{y}|=2\)
Answer & Solution
Correct Answer
(A) \(|\vec{x}|=|\vec{y}|\)
Step-by-step Solution
Detailed explanation
\(\begin{gathered}|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2} \\ \vec{a} \vec{b}=|\vec{a}||\vec{b}| \cos \theta=\sqrt{2} \times \sqrt{2} \times \frac{1}{2}=1\end{gathered}\)…
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