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Chapter 12 Introduction to 3 dimensional Geometry

After the knowledge of 2d geometry, it is time to add a new dimension to the geometry after that it is called 3d geometry. This is just an introduction but details of this chapter is in the next class. This chapter is for basics. This chapter consists of coordinate axis and coordinate planes in three dimensions, coordinates of a point, distance between two points and section formula.

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Exercise 1

  • Q1 A point is on the x-axis. What are its y-coordinates and z-coordinates?
    Ans:

    If a point is on the x-axis, then its y-coordinates and z-coordinates are zero.
    Q2 A point is in the XZ-plane. What can you say about its y-coordinate?
    Ans:

    If a point is in the XZ plane, then its y-coordinate is zero.
    Q3 Name the octants in which the following points lie: (1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)
    Ans:

    The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I.

    The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, 3) are positive, negative, and positive respectively. Therefore, this point lies in octant IV.

    The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, –5) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

    The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, –5) are positive, positive, and negative respectively. Therefore, this point lies in octant V.

    The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, –5) are negative, positive, and negative respectively. Therefore, this point lies in octant VI.

    The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, 5) are negative, positive, and positive respectively. Therefore, this point lies in octant II.

    The x-coordinate, y-coordinate, and z-coordinate of point (–3, –1, 6) are negative, negative, and positive respectively. Therefore, this point lies in octant III.

    The x-coordinate, y-coordinate, and z-coordinate of point (2, –4, –7) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

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