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Quiz/worksheet #2 MAT 309-
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Please show ALL of your work clearly and neatly. No work = No credit. Your group size may have AT MOST 3 people.
- Find parametric equations for the following lines:
(a) The line through (4, − 1 , 2) and (1, 1 , 5)
(b) The line through (1, 0 , −1) and parallel to the line 13 (x − 4) = 12 y = z + 2
(c) The line through (− 2 , 2 , 4) and perpendicular to the plane 2x − y + 5z = 12
- Find an equation for each of the following plane:
(a) The plane through (1, − 2 , 3) and parallel to 4x + 5y − 6 z = 7
(b) The plane through (1, 0 , −1), (0, 1 , −1), and (− 1 , 1 , 0)
(c) The plane through (1, 2 , −1) that contains the line x = 2t, y = 3 − t, z = 1 + 3t
- The rectangular coordinates of a point are (2, 2 , −1). Find the cylindrical and spherical coordinates of the point.
- Write the equation in cylindrical and spherical coordinates:
(a) x^2 + y^2 + z^2 = 1 (b) x^2 + y^2 + z^2 = 2x
