Section 12.5: Lines & Planes

Let \(L_1\) be the line through the points \((1, 2, 6)\) and \((2, 4, 8)\). Let \(L_2\) be the line of intersection of the planes \(\mathcal{P}_1\) and \(\mathcal{P}_2\), where \(\mathcal{P}_1\) is the plane \(x - y + 2z + 1 = 0\) and \(\mathcal{P}_2\) is the plane through the points \((3, 2, -1), (0, 0, 1),\) and \((1, 2, 1)\). Calculate the distance between \(L_1\) and \(L_2\).