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

In summary, Homework Equations: Yes, vectors in different planes add up to give a zero resultant. However this is not a sufficient condition to satisfy the problem.
  • #1
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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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  • #2
pl reply me
 
  • #3
Hi xphloem,

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

[tex]
\begin{align}
\vec A &= (1,1,0)\nonumber\\
\vec B &= (-1,0,1)\nonumber\\
\vec C &= (0,-1,-1)\nonumber
\end{align}
[/tex]

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?
 
  • #4
alphysicist said:
Hi xphloem,

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

[tex]
\begin{align}
\vec A &= (1,1,0)\nonumber\\
\vec B &= (-1,0,1)\nonumber\\
\vec C &= (0,-1,-1)\nonumber
\end{align}
[/tex]

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?
 
  • #5
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..
 

1. What is the concept of vectors in different planes adding up to a zero resultant?

This concept states that when two or more vectors are added together, their magnitudes and directions must be taken into account. If the vectors are in different planes, their components along a common axis must be added together in order to determine the resultant vector. If the sum of these components is zero, then the resultant vector will also be zero.

2. How do you calculate the resultant vector for vectors in different planes?

To calculate the resultant vector, you must first find the components of each vector along a common axis. Then, simply add these components together to get the resultant vector. If the sum of the components is zero, then the resultant vector will also be zero.

3. What is the significance of the zero resultant in vectors in different planes?

The zero resultant in vectors in different planes indicates that the vectors are canceling each other out. This means that the combined effect of the vectors is zero, and there is no net displacement or force in any direction.

4. Can two vectors in different planes ever have a non-zero resultant?

Yes, it is possible for two vectors in different planes to have a non-zero resultant. This will occur when the components of the vectors along a common axis do not cancel out completely, resulting in a non-zero value for the resultant vector.

5. How does the angle between vectors in different planes affect the resultant vector?

The angle between vectors in different planes has no effect on the magnitude of the resultant vector. However, it does affect the direction of the resultant vector. The resultant vector will be in the same plane as the vectors being added, and its direction will be determined by the angle between the vectors.

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