Vector Algebra: JEE Main 2021 Mathematics question

Let $\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow b$ and $\overrightarrow c = \widehat j - \widehat k$ be three vectors such that $\overrightarrow a \times \overrightarrow b = \overrightarrow c$ and $\overrightarrow a \,.\,\overrightarrow b = 1$. If the length of projection vector of the vector $\overrightarrow b$ on the vector $\overrightarrow a \times \overrightarrow c$ is l, then the value of 3l² is equal to _____________.