Can Cosine Affect Whether Three Nonzero Vectors Must Lie in the Same Plane?

[yosheey]

If there are three nonzero vectors..
Do you think cosine effects this example:show the three vectors must lie in the same plane?
-------------
* -->dot product
X -->cross product
--------------
A*(BXC)=0

so we can change as..

|A||B||C|sin[tex]\alpha[/tex]cos[tex]\beta[/tex]=0

then... we can meet

sin[tex]\alpha[/tex]cos[tex]\beta[/tex]=0

so ...

Exactly sin can make vectors lie in same plane if sin=0 (because three of two vectors have same direction...)
but I'm not sure cos effects...?

 

[Dr.D]

Do you know the direction of the vector that results from a cross product?

Do you know how to write, in vector form, that two vectors are perpendicular to each other?

Don't worry so much about sine and cosine effects per se, but think about the two questions above. They are the answer to your problem.

 

[tiny-tim]

|A||B||C|sin[tex]\alpha[/tex]cos[tex]\beta[/tex]=0

Hi yosheey!

Your approach is fundamentally wrong, because that equation only deals with the magnitude of the final result.

You must use a method that deals with the directions of the intermediate stages.