3-D coordinate systems problem

In summary, The conversation is about determining whether points lie on a straight line. The first set of points (A, B, C) are given and the second set of points (K, L, M) are also mentioned. The question is whether to draw a graph and find the slopes or approach the problem in a different way. The person asking for help has done well in Calculus I and II, but is struggling with Calculus III. The advice given is to compare the slopes of the lines passing through the points. Graphing the points is not necessary for this problem.
  • #1
bochai
4
0
Pleas help me with this exercises(this is not a homework):

Determine whether the points lie on a straight line.

a) A(5,1,3), B(7,9,-1), C(1,-15,11)

b) K(0,3,-4) L(1,2,-2), M(3,0,1)

Should I draw the graph, then find the slopes?
Or is there any other way to approach?
Pleas help!
By the way, I got straight A's for Calc I,II. and every body keep telling me that Calc III is easier compare to Calc II. but, I feel it's so hard, and I don't know what to do. can some one give me some advice?thanks.
 
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  • #2
If they're on a line, the vectors seperating each pair of points are scalar multiples of each other.
 
  • #3
The simplest way is to do just what you said: Find the slope of the line through A and B and the slope of the line through B and C. They are the same line if and only if they have the same slope. Same for the second problem. Since the problem doesn't require you to graph them, that's not necessary.
 

Related to 3-D coordinate systems problem

1. What is a 3-D coordinate system problem?

A 3-D coordinate system problem is a mathematical question that involves finding the location of a point in a three-dimensional space using three coordinates: x, y, and z. It is commonly used in geometry, physics, and engineering to describe the position of objects in a three-dimensional space.

2. How do you solve a 3-D coordinate system problem?

To solve a 3-D coordinate system problem, you need to first identify the three coordinates of the point in the three-dimensional space. Then, you can use the Pythagorean theorem and trigonometric functions to calculate the distance and angles between the point and the axes. Finally, you can plot the point on a three-dimensional graph to visualize its location.

3. What are the applications of 3-D coordinate systems?

3-D coordinate systems are used in various fields such as computer graphics, computer-aided design (CAD), 3-D modeling, and virtual reality. They are also used in real-world applications such as GPS navigation, robotics, and satellite imaging.

4. What are the main components of a 3-D coordinate system?

A 3-D coordinate system has three main components: the x-axis, y-axis, and z-axis. The x-axis is the horizontal axis, the y-axis is the vertical axis, and the z-axis is the depth axis. These three axes intersect at a point called the origin, which is usually denoted as (0,0,0).

5. Can you convert a 3-D coordinate system problem into a 2-D coordinate system problem?

Yes, it is possible to convert a 3-D coordinate system problem into a 2-D coordinate system problem. This can be done by projecting the three-dimensional space onto a two-dimensional plane. However, this conversion may result in a loss of information, so it is not always a suitable solution.

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