Decide whether \((1,2,2)\) and \((2,-1,0)\) are orthogonal.

Find \(\cos\theta\), where \(\theta\) is the angle between \(\mathbf u=(1,0,1)\) and \(\mathbf v=(2,1,0)\).

Find all real \(t\) such that \((t,1,2)\) is orthogonal to \((3,-4,1)\).

Show that \(\mathbf u=(1,1,0)\) and \(\mathbf v=(1,-1,0)\) meet at a right angle, then find the angle between them.