Vector Algebra

If \(\bar{p}=\hat{i}+\hat{j}+\hat{k}\) and \(\bar{q}=\hat{i}-2 \hat{j}+\hat{k}\). Then a vector of magnitude \(5 \sqrt{3}\) units perpendicular to the vector \(\bar{q}\) and coplanar with \(\bar{p}\) and \(\bar{q}\) is