JEE Main 2021 (31 Aug, Shift 2) Maths Q75: Triple Products

Question

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors mutually perpendicular to each other and have same magnitude. If a vector $\vec{r}$ satisfies
$\vec{a}	imes\left\{(\vec{r}-\vec{b})	imes\vec{a}ight\}+\vec{b}	imes\left\{(\vec{r}-\vec{c})	imes\vec{b}ight\}+\vec{c}	imes\left\{(\vec{r}-\vec{a})	imes\vec{c}ight\} = \vec{0}$, then $\vec{r}$ is equal to :

Accepted Answer

Option 2: $\frac{1}{2}\left(\vec{a}+\vec{b}+\vec{c}\right)$

Answer

$\frac{1}{2}\left(\vec{a}+\vec{b}+2\vec{c}\right)$

Answer

$\frac{1}{2}\left(\vec{a}+\vec{b}+\vec{c}\right)$

Answer

$\frac{1}{3}\left(\vec{a}+\vec{b}+\vec{c}\right)$

Answer

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

JEE Main 31 August 2021, Shift 2, Maths Q75

Same idea in other shifts