Question:medium

$\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar and mutually perpendicular vectors of same magnitude K. $\vec{r}$ is any vector satisfying $\vec{a}\times((\vec{r}-\vec{b})\times\vec{a}) + \vec{b}\times((\vec{r}-\vec{c})\times\vec{b}) + \vec{c}\times((\vec{r}-\vec{a})\times\vec{c}) = \vec{0}$, then $\vec{r} =$

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The vector triple product identity $\vec{A}\times(\vec{B}\times\vec{C}) = (\vec{A}\cdot\vec{C})\vec{B} - (\vec{A}\cdot\vec{B})\vec{C}$ is crucial for simplifying nested cross products. Also, remember the formula for expressing any vector in terms of an orthogonal basis.

Updated On: Mar 30, 2026

$\frac{K^2(\vec{a}+\vec{b}+\vec{c})}{3K^2-1}$
$\frac{\vec{a}+\vec{b}+\vec{c}}{2}$
$\frac{K(\vec{a}+\vec{b}+\vec{c})}{K+1}$
$\frac{\vec{a}+\vec{b}+\vec{c}}{K^2+1}$

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The Correct Option is B

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