MAT 307 Midterm: MAT 307 SBU Fall 10 Exam 1Solutions

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 307
• Professor: All

Document Summary

Find the point of intersection of the lines h2 + t, 1 2t, 4 + ti and h 1 2s, 1 + s, 1 3si. Solution: we need to determine for which value of s and t the three coordinates are equal. That is, we need to solve the following linear system: 1 2t = 1 + s. From the second equation, we have s = 2t. 2 + t = 1 + 4t, and so t = 1. Thus, the rst two equations give t = 1, s = 2. We have to con rm that this is consitent with the third equation. The point of intersection is then obtained by plugging in to either line, giving (3, 3, 5) as the point where they cross. Write the equation of the plane containing the two lines h2 + t, 1 2t, 4 + ti and h 1 2s, 1 + s, 1 3si.