Let \(\vec{a}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{b}=\vec{a} \times(\hat{i}-2 \hat{k})\) and \(\vec{c}=\vec{b} \times \hat…

Let \(\vec{a}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{b}=\vec{a} \times(\hat{i}-2 \hat{k})\) and \(\vec{c}=\vec{b} \times \hat{k}\). Then the projection of \(\vec{c}-2 \hat{j}\) on \(\vec{a}\) is :

[JEE Main 2025, 24 Jan (Shift 2)]