Let \(\vec{a}=4 \hat{i}+3 \hat{j}\) and \(\vec{b}=3 \hat{i}-4 \hat{j}+5 \hat{k}\) and \(\vec{c}\) is a vector such that …

Let \(\vec{a}=4 \hat{i}+3 \hat{j}\) and \(\vec{b}=3 \hat{i}-4 \hat{j}+5 \hat{k}\) and \(\vec{c}\) is a vector such that \(\vec{c} \cdot(\vec{a} \times \vec{b})+25=0, \vec{c} \cdot(\hat{i}+\hat{j}+\hat{k})=4\) and projection of \(\vec{c}\) on \(\vec{a}\) is 1 , then the projection of \(\vec{c}\) on \(\vec{b}\) equals:

[JEE Main 2023, 29 Jan (Shift 2)]