Let a =4 i +3 j and b =3 i -4 j +5 k. If c is a vector such that c ·( a × b )+25=0, c ·( i + j + k )=4, and projection of c on a is 1, then the…

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