Cartesian 3D Vector Plotting Points?

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SUMMARY

This discussion focuses on plotting points in a Cartesian 3D space, specifically the point B(-2,3,5). The user clarifies that movements along the x, y, and z axes are independent, meaning that moving in one direction does not affect the others. Additionally, the conversation addresses finding the equation of a plane defined by three points: (-3,0,0), (4,-2,0), and (0,3,-5). The solution involves calculating a normal vector using the cross product of two vectors formed by these points, leading to the equation 10x + 35y + 27z + 30 = 0.

PREREQUISITES
  • Understanding of Cartesian coordinates
  • Knowledge of vector operations, specifically cross product
  • Familiarity with equations of planes in 3D space
  • Basic proficiency in calculus, particularly in multivariable contexts
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Students in calculus or geometry courses, educators teaching 3D plotting, and anyone interested in understanding vector mathematics and plane equations in three-dimensional space.

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Homework Statement


Plot the following point:
B(-2,3,5)




The Attempt at a Solution


If I were to plot (-2,3,5), when I make my first movement of -2, it does not move anywhere on the y-axis correct and when I am moving on my Y axis, There is no movement in the z axis?
 
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In Cartesian coordinates (-2,3,5) is the same thing as saying "-2 in the x-direction, 3 in the y-direction, and 5 in the z-direction". As movement in the x,y,z-directions don't affect the other directions, so yeah...although note that if you're moving on the y-axis, you're not only not moving on the z-axis, but you're also not moving on the x-axis.

So it's "move -2 on the x-axis, move 3 on the y-axis, move 5 on the z-axis".
 
Ok thank you, can you give me some help on this:

What is the axis or plane these points would lie:

(-3,0,0) (4,-2,0) and (0,3,-5)
 
If you're unsure about how to plot a point in 3D space, I'm not too sure how I'm going to explain to you how to find the equation of a plane from three points.

Open your calc 3 book and get to reading.

The way I would do it is find a normal vector for the plane by taking a cross product of two vectors defined by those points and then dotting that normal vector with a vector in the plane and setting it to zero...

You need to go and learn the material. The answer is 10x + 35y + 27z + 30 = 0, if you need to check yourself.
 
Last edited:

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