Two particles are located at equal distance from origin. The position vectors of those are represented by \( \,\vec{A} = 2\hat{i} + 3n\hat{j} + 2\hat{k} \, \) and \( \,\vec{B} = 2\hat{i} - 2\hat{j} + 4p \hat{k} \, \), respectively. If both the vectors are at right angle to each other, the value of \( n^{-1} \) is ________.
