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

[xphloem]

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?

 

[xphloem]

pl reply me

 

[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?

 

[xphloem]

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?

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?

 

[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..