Let a =3 i + j -2 k, b =4 i + j +7 k and c = i -3 j +4 k be three vectors. If a vectors p satisfies p × b = c × b and p · a =0, then p ·( i - j - k )…

Let $\displaystyle \vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=4 \hat{i}+\hat{j}+7 \hat{k}$ and $\displaystyle \vec{c}=\hat{i}-3 \hat{j}+4 \hat{k}$ be three vectors. If a vectors $\displaystyle \vec{p}$ satisfies $\displaystyle \vec{p} \times \vec{b}=\vec{c} \times \vec{b}$ and $\displaystyle \vec{p} \cdot \vec{a}=0$, then $\displaystyle \vec{p} \cdot(\hat{i}-\hat{j}-\hat{k})$ is equal to