Cho ba vectơ \(\overrightarrow{m}=\left(-5;4;9\right),\overrightarrow{n}=\left(2;-7;0\right),\overrightarrow{p}=\left(6;3;-4\right)\).
a) Tính \(\overrightarrow{m}.\overrightarrow{n},\overrightarrow{m}.\overrightarrow{p}\).
b) Tính \(\left|\overrightarrow{m}\right|,\left|\overrightarrow{n}\right|,\cos\left(\overrightarrow{m},\overrightarrow{n}\right)\).
c) Cho \(\overrightarrow{q}=\left(1;-2;0\right)\). Vectơ \(\overrightarrow{q}\) có vuông góc với \(\overrightarrow{p}\) không?