Section 12.5 – Equations of Lines and Planes
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Find an equation of the plane passing through the point \((1,5,-3)\) and perpendicular to the line \(x= 2-4t\), \(y=2t\), \(z=-1+t.\)
\(-4x+2y+z=3\) (or some scalar multiple of this)
2. Find the point at which the given lines \(\mathbf{r}_1(t) = \left< 2+t, 2t, 5+t \right>\) and \(\mathbf{r}_2(s) = \left< s, -4+4s, 3+s \right>\) intersect.
\((0,-4,3)\)
3. The lines \(\mathbf{r}_1(t) = \left< 2+t, 2t, 5+t \right>\) and \(\mathbf{r}_2(s) = \left< s, -4+4s, 3+s \right>\) intersect at \((0,-4,3)\). Find an equation of the plane that contains these lines.
\(-2x+2z=6\) (or some scalar multiple of this)