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M273 - Fall 2017 Take Home 1 Name:

Problem 1. Find an equation of the line passing through (−2, 4, 5) and parallel to the vector 〈3,−1, 6〉

Problem 2. Find an equation for the line passing through the points (3, 1,−1) and (3, 2,−6)

Problem 3. Show that the line through the points (0, 1, 1) and (1,−1, 6) is perpendicular to the line through the points (−4, 2, 1) and (−1, 6, 2)

Problem 4. Find an equation of the plane passing through the point (−5, 1, 2) and with normal vector 〈3,−5, 2〉

Problem 5. Find an equation of the plane passing through the point (3, 0, 8) and parallel to 2x+5y+8z = 17

Problem 6. Find an equation of the plane passing through the three points (−1, 1,−1), (1,−1, 2), and (4, 0, 3)

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Problem 7. Find an equation of the plane that passes through the point (1, 6,−4) and contains the line x = 1 + 2t, y = 2−3t, and z = 3− t

Problem 8. Find the point at which the line x = 1 + t, y = 2t, z = 3t intersects the plane x + y + z = 1

Problem 9. Find the equation of the plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t and is parallel to the plane 5x + 2y + z = 1

Problem 10. Find an equation of the plane that passes through (1, 5, 1) and is perpendicular to the planes x + 3z = 4 and 2x + y −2z = 2

Problem 11. Find the equation of the plane that passes through the line of intersection of the planes x−z = 1, y + 2z = 3 and is perpendicular to the plane x + y −2z = 1

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