MAT 228 Midterm: F05mt1sol

• School: University of Maine
• Department: Mathematics and Statistics
• Course: MAT 228
• Professor: All

Document Summary

October 7, 2005: (12 pts) do the following. (a) Carefully sketch ~v + ~w: (b) carefully sketch ~w ~v: w w v+w v. Carefully sketch proj~v ~w (the projection of ~w onto ~v). w proj w v v. 1: (15 pts) let l be the line given by the following parametric equations: x = 1 + 2t, y = 1 t, z = 3t. Find an equation for the plane through ( 1, 1, 1) and perpendicular to l. The line l can be written hx, y, zi = h1, 1, 0i + th2, 1, 3i . Note h2, 1, 3i is a direction vector for the line, so it is perpendicular to the plane we want. Thus we take ~n = h2, 1, 3i, and using ~n (~r ~r0) = 0, our plane is which gives h2, 1, 3i hx + 1, y 1, z + 1i = 0,