Math Problem Statement

  1. Plot each of the following points in xyz-space: A = (0, 4, −1) B = (1, 2, 5) C = (−3, 0, 0) D = (−5, −1, 2)

Solution

Here is the 3D plot of the points A=(0,4,1)A = (0, 4, -1), B=(1,2,5)B = (1, 2, 5), C=(3,0,0)C = (-3, 0, 0), and D=(5,1,2)D = (-5, -1, 2) in xyz-space. Each point is labeled with its corresponding letter.

If you have any questions about this plot or need further assistance, feel free to ask!

Here are 5 related questions you might consider:

  1. How would the plot change if the point AA were moved to (0,4,2)(0, 4, 2)?
  2. What is the distance between points AA and BB in xyz-space?
  3. How do you determine the equation of the plane passing through points AA, BB, and CC?
  4. What is the midpoint of the line segment connecting points CC and DD?
  5. How would you describe the vector AB\overrightarrow{AB} in component form?

Tip: When working in 3D space, visualizing points, lines, and planes can be greatly aided by plotting, helping you understand their relationships.