Let \(P_1 = (1,2,-1)\) and \(P_2 = (-2,1,-2)\text{,}\) and let \(\mathcal{L}\) be the line in \(\R^3\) through \(P_1\) and \(P_2\text{.}\) (This is the same line as in Activity 9.5.2.)
Do the lines \(\mathcal{L}\) and \(\mathcal{K}\) intersect? If so, provide the point of intersection and the \(t\) and \(s\) values, respectively, that result in the point. If not, explain why. To find a point of intersection, you can set the coordinate equations of each line equal to each other try to solve for \(t\) and \(s\text{.}\)
Remember that the two lines need to go through the same \((x,y,z)\) point but do not need to have the same parameter value at that point (which is why we used different variable names for the parameters \(t\) and \(s\)).
