Two particles are located at equal distance from origin. The position vectors of those are represented by Ā=2 i +3 n j +2 k and B̄=2 i -2 j +4 p k,…

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