M273 – Fall 2017 Take Home 1

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 h3, −1, 6i 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 h3, −5, 2i 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) 1 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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