設 $a,b,c,d,r,s,t$ 皆為實數，已知坐標空間中三個非零向量 $\overrightarrow u = (a,b,0)$、$\overrightarrow {\nu} = (c,d,0)$ 及 $\overrightarrow w = (r,s,t)$ 滿足內積 $\overrightarrow w \cdot \overrightarrow u = \overrightarrow w \cdot \overrightarrow \nu = 0$。考慮三階方陣 $A = \left[\begin{array}{l l l}{a}&{b}&{0}\\ {c}&{d}&{0}\\ {r}&{s}&{t}\end{array}\right]$，試選出正確的選項。