Vectors in different planes add up to give a zero resultant?

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Homework Help Overview

The discussion revolves around the question of whether three or four vectors in different planes can add up to give a zero resultant. The original poster presents a scenario involving vector components in three-dimensional space.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the possibility of vectors in different planes summing to zero, with attempts to resolve vectors into their components. Questions arise about the definitions of planes and how vectors can interact within those planes.

Discussion Status

Some participants have provided examples of vectors that add to zero but are constrained to a single plane, prompting further inquiry into the conditions under which vectors in different planes can achieve a zero resultant. There is an ongoing exploration of how vectors can be positioned in relation to one another.

Contextual Notes

Participants are discussing the implications of vector placement in three-dimensional space, including the concept of 'crooked' planes versus standard coordinate planes. The original poster's assumptions about vector components and their arrangement are being questioned.

xphloem
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Homework Statement



Can
1. three
2. four
vectors in different planes add up to give a zero resultant?


Homework Equations





The Attempt at a Solution



1. Yes.
2. Yes.

1. suppose that we resolve the 3 vectors in i,j,k components. Putting each one of them zero in the respective three vectors to make them in 3 separate plane. Cant they be zero?
2. similar as above. the only thing is that the fourth vector has none of its components zero.



Am I right?
 
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Hi xphloem,

For #1, were you thinking of something like this:

<br /> \begin{align}<br /> \vec A &amp;= (1,1,0)\nonumber\\<br /> \vec B &amp;= (-1,0,1)\nonumber\\<br /> \vec C &amp;= (0,-1,-1)\nonumber<br /> \end{align}<br />

They definitely add to zero, but they are in a single plane, so they don't satisfy the requirements of the problem.

For this problem: if you start with any two vectors, they define a plane. Then you want a third vector that is not in that same plane. Can those add to zero?
 
alphysicist said:
Hi xphloem,

For #1, were you thinking of something like this:

<br /> \begin{align}<br /> \vec A &amp;= (1,1,0)\nonumber\\<br /> \vec B &amp;= (-1,0,1)\nonumber\\<br /> \vec C &amp;= (0,-1,-1)\nonumber<br /> \end{align}<br />

They definitely add to zero, but they are in a single plane, so they don't satisfy the requirements of the problem.

For this problem: if you start with any two vectors, they define a plane. Then you want a third vector that is not in that same plane. Can those add to zero?

How can all of them be in one plane
the first on is in xy plane
second one in xz plane
and the third in yz plane
am I wrong?
 
The three (essentially only 2) vectors A, B and C together form a 'new' plane, not like the xy, xz or yz plane, but you can also have a 'crooked' plane for example. Then they are still in the same plane, even though the plane is not the xy, yz or zx plane..
 

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