If \(\vec{a}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k}, \vec{b}=3 \hat{\imath}+\hat{\jmath}-\hat{k}\) and \(\vec{c}\) is cop…

If \(\vec{a}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k}, \vec{b}=3 \hat{\imath}+\hat{\jmath}-\hat{k}\) and \(\vec{c}\) is coplanar with \(\vec{a}\) and \(\vec{b}\). Also \(\vec{a} \cdot \vec{c}=5\) and \(\vec{c}\) is perpendicular to \(\vec{b}\). Then \(|\vec{c}|\) is (24 Jan, Shift I, Memory Based)