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

Compute the scalar triple product \(\mathbf a\cdot(\mathbf b\times\mathbf c)\) for \(\mathbf a=(1,2,0)\), \(\mathbf b=(0,1,3)\), and \(\mathbf c=(2,0,1)\).

Use a scalar triple product to find the volume of the parallelepiped spanned by \((1,0,2)\), \((0,3,1)\), and \((2,1,0)\).

Decide whether \((1,2,3)\), \((2,4,6)\), and \((0,1,1)\) are coplanar as vectors from the origin.