Compute the scalar product \((2,-1,3)\cdot(4,5,-2)\).

Let \(\mathbf u=(1,2,-2)\). Compute \(\mathbf u\cdot\mathbf u\).

Find all real \(t\) such that \((t,1,2)\cdot(3,-1,4)=10\).

Use the scalar product to decide whether \(\mathbf a=(2,-1,1)\) and \(\mathbf b=(1,3,1)\) are orthogonal.