Compute \((1,0,0)\times(0,1,0)\).

Compute \((2,1,0)\times(0,3,4)\).

Verify that \((1,2,3)\times(2,0,1)\) is orthogonal to \((1,2,3)\).

Find the area of the parallelogram spanned by \(\mathbf a=(1,0,2)\) and \(\mathbf b=(0,3,1)\).