Question:medium

\( \bar{a}, \bar{b}, \bar{c} \) are three unit vectors such that \( x\bar{a} + y\bar{b} + z\bar{c} = p(\bar{b} \times \bar{c}) + q(\bar{c} \times \bar{a}) + r(\bar{a} \times \bar{b}) \). If \( (\bar{a},\bar{b})=(\bar{b},\bar{c})=(\bar{c},\bar{a})=\frac{\pi}{3} \), \( (\bar{a}, \bar{b} \times \bar{c})=\frac{\pi}{6} \) and \( \bar{a}, \bar{b}, \bar{c} \) form a right-handed system, then \( \frac{x+y+z}{p+q+r} = \)

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Summing symmetric equations simplifies the problem of finding sums of variables.

Updated On: Mar 26, 2026

\( \frac{3}{4} \)
\( \frac{1}{\sqrt{2}} \)
\( 2\sqrt{2} \)
\( \frac{3}{8} \)

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The Correct Option is D

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