QJEEM24Ma6f20: JEE Main 2024 Physics - Class 11 JEEM24Ma6f20 Solution: Let and be a vector such that . If , then is equal to __________.

$(\vec{a}+2 \vec{b}) \times \vec{c}=3(\vec{c} \times \vec{a})$

$\begin{aligned}\Rightarrow \quad & \vec{b} \times \vec{c}+2(\vec{a} \times \vec{c})=0 \\& (\vec{b}+2 \vec{a}) \times \vec{c}=0 \\& \vec{c}=\lambda(\vec{b}+2 \vec{a}) \\& \vec{c} \cdot \vec{a}=130 \Rightarrow \lambda=1 \\& \vec{c}=4 \hat{i}-7 \hat{j}+15 \hat{k} \\& \vec{b} . \vec{c}=30\end{aligned}$