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ConcepTest • Section 12.1 • Question 1

ConcepTest • Section 12.1 • Question 1. Look at the room you are in. Put a coordinate system in the room so that one corner is the origin. Find equations of the planes that describe all walls, the floor and the ceiling. ANSWER. ConcepTest • Section 12.1 • Answer 1.

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ConcepTest • Section 12.1 • Question 1

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  1. ConcepTest• Section 12.1 •Question 1 Look at the room you are in. Put a coordinate system in the room so that one corner is the origin. Find equations of the planes that describe all walls, the floor and the ceiling.

  2. ANSWER ConcepTest• Section 12.1 •Answer 1 The answer depends on the room, the choice of coordinate axes, and unit of distance. COMMENT: There will probably be a discussion on which corner to pick for the origin and what directions are x and y. As a follow-up question, ask for coordinates of certain points inside and outside of the classroom.

  3. Which of the points A = (3, 0, 3), B = (0, 4, 2), C = (2, 4, 1), and D = (2, 3, 4) lies closest to ConcepTest• Section 12.1 •Question 2 • the xy-plane? • the origin? • the y-axis? • the point (1, 2, 3)?

  4. ANSWER ConcepTest• Section 12.1 •Answer 2 C is closest to the xy-plane, since the distance to the xy-plane is |z|. A is closest to the origin, since the distance to the origin is B is closest to the y-axis, since the distance to the y-axis is D is closest to the point (1, 2, 3), since the distance to (1, 2, 3) is COMMENT: Ask the students to plot the four points.

  5. ConcepTest• Section 12.1 •Question 3 In words, describe the surface given by the equation

  6. ANSWER ConcepTest• Section 12.1 •Answer 3 A sphere of radius 5 centered at (1, -2, -5). COMMENT: It is helpful to students to be able to recognize the equation for a sphere, a cylinder, a cone, and a paraboloid.

  7. Sphere A is centered at the origin and the point (0, 0, 3) lies on it. Sphere B is given by the equation x2 + y2 + z2 = 3. ConcepTest• Section 12.1 •Question 4 • A encloses B • B encloses A • A and B are equal • None of the above

  8. ANSWER ConcepTest• Section 12.1 •Answer 4 • Both spheres are centered at the origin. Sphere A has radius 3, sphere B has radius • Thus, A encloses B. COMMENT: Follow-up Question. How would you change the equations of the spheres so that each of the other three choices happens?

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