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

1. May 9, 2008

### xphloem

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?

2. May 9, 2008

### xphloem

3. May 10, 2008

### alphysicist

Hi xphloem,

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

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

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. May 12, 2008

### xphloem

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. May 12, 2008

### Nick89

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..