Let 𝑎 and 𝑏 be positive real numbers. Suppose $$\overrightarrow{PQ} = a\hat{i} + b\hat{j}$$ and $$\overrightarrow{PS} = a\hat{i} - b\hat{j} $$ are adjacent sides of a parallelogram 𝑃𝑄𝑅𝑆. Let $$\overrightarrow{u}$$ and \overrightarrow{v} be the projection vectors of $$\overrightarrow{u} = \hat{i} + \hat{j}$$ along $$\overrightarrow{PQ}$$ and $$\overrightarrow{PS}$$, respectively. If $$\mid \overrightarrow{u}\mid + \mid \overrightarrow{v} \mid = \mid \overrightarrow{w} \mid$$ and if the area of the parallelogram 𝑃𝑄𝑅𝑆 is 8, then which of the following statements is/are TRUE?