Now equate the coordinates of H to get the fourth point.

In summary, the conversation discusses finding the fourth point of a parallelogram given three points. The methods of using vectors and adding the points together are mentioned, with the suggestion to use the point in the middle as a reference point. It is later suggested to use the center point of the parallelogram to find the fourth point.
  • #1
skiboka33
59
0
I wasn't sure what category to put this in, but here's my problem.

There is a parallelogram with 3 given points for its corners (each with 3 different coordinates). The idea is to find the forth point. I've tried subbing (x,y,z) for the unknown point, and creating 4 vectors. I tried equating the cross product of two opposite vectors to zero as well as absolute value of opposite vectors to each other. This left me with a lot of algebra after I combined both methods and then cheated to get a decimal answer which I'm not even sure is correct. Is there an easier way to do this problem that I'm missing? Thanks.
 
Mathematics news on Phys.org
  • #2
What was the geometric motivation for adding vectors in the manner that we do ?
 
  • #3
Given three points, there are three possible solutions to you problem, depending on which point is the "middle" point. Let the three points be A,B,C and let A be the "middle". The the fourth point is given by A+(B-A)+(C-A)=B+C-A.
 
  • #4
mathman said:
Given three points, there are three possible solutions to you problem, depending on which point is the "middle" point. Let the three points be A,B,C and let A be the "middle". The the fourth point is given by A+(B-A)+(C-A)=B+C-A.

hmm.. that sounds much easier. Well say there are three points A,B,C and point D is diagonally opposite A, does that mean that D is the point that does not connect to A? Thanks for the help by the way.

That also gave me another similar idea. Shouldn't A + B + C + D = 0, and therefore the components of each should sum to zero?

EDIT: just realized that that's what you did :rolleyes:
 
Last edited:
  • #5
A+D=B+C is the result I have where A is opposite D.

One easy way to see it is by considering the point H at the center of the parallelogram.

H=(A+D)/2
H=(B+C)/2
 
Last edited:

What is a parallelogram in 3D space?

A parallelogram in 3D space is a flat shape with four sides and four vertices that lie on the same plane. It is a three-dimensional version of a parallelogram in 2D space.

What are the properties of a parallelogram in 3D space?

A parallelogram in 3D space has four sides of equal length and four angles of equal measure. It also has two pairs of parallel sides and opposite sides are equal in length.

How do you calculate the area of a parallelogram in 3D space?

The area of a parallelogram in 3D space can be calculated by multiplying the length of one side by the perpendicular distance from that side to the opposite side. This can also be written as A = base × height.

How do you find the volume of a parallelogram in 3D space?

The volume of a parallelogram in 3D space can be calculated by multiplying the area of the base by the height of the parallelogram. This can also be written as V = base area × height.

What is the difference between a parallelogram and a rectangle in 3D space?

A parallelogram and a rectangle both have four sides and four angles, but the angles of a parallelogram do not have to be right angles like in a rectangle. Additionally, a parallelogram does not have to have all sides of equal length like a rectangle does.

Similar threads

  • General Math
Replies
3
Views
2K
Replies
20
Views
3K
  • General Math
Replies
11
Views
1K
Replies
3
Views
95
Replies
5
Views
2K
  • General Math
Replies
4
Views
872
  • Precalculus Mathematics Homework Help
Replies
17
Views
907
Replies
6
Views
826
Replies
6
Views
3K
  • Precalculus Mathematics Homework Help
Replies
18
Views
460
Back
Top