Problem Set 5: Finding Equations for Planes and Lines, Assignments of Analytical Geometry and Calculus

Download Problem Set 5: Finding Equations for Planes and Lines and more Assignments Analytical Geometry and Calculus in PDF only on Docsity! Problem Set 5, Due Sixth Class Meeting (1) Find an equation for the plane passing through the points (1, 3, 4), (2, 7, 5) and (6, 11, 5). How far is the point (3, 6,−4) from this plane? Find an equation for the line passing through (3, 6,−4) and that is perpendicular to this plane. Where do this line and plane intersect? Now use the dis- tance formula between points to confirm that the distance you computed is correct. (2) Find an equation for the plane tangent to the sphere x2 + 2x + y2 + 4y + z2 − 6z = 15 at the point (1, 1,−1) on the sphere. Remember that radial lines are perpendicular to spheres. 1