Understanding Cross Product

[RedSquirrel]

Hi, I hope this is the right sub-forum for my question.

The question is about cross product, I have no former knowledge about cross products but I'm trying to understand.

From what I know the right angle vector is the cross product of the other two vectors once multiplied. If the vectors are perpendicular to the right angle that would make the value 1, if they are not perpendicular that would make the value 0. To understand my explanation more clearly, suppose you have a roof of a house, most roofs are angled, depending how much the right angle is multiplied from the two vectors and how much they are perpendicular some areas on the roof will be less black, considering it's a black roof and as it's less perpendicular most if not all of the roof won't be black ?

I hope the above explanation is clear and I hope it more or less explains cross products ?

 

[pka]

The question is about cross product, I have no former knowledge about cross products but I'm trying to understand.

It is ridiculous to try to understand anything if you don't fully understand the definition.
Any two non-zero vectors form an angle. Suppose that \(\displaystyle \vec{v}~\&~\vec{w}\) are two non-zero vectors and
\(\displaystyle \theta\) is the angle between them. Then the cross-product \(\displaystyle \vec{v}\times\vec{w}\) is a vector that is perpendicular to both \(\displaystyle \vec{v}~\&~\vec{w}\) that has length \(\displaystyle \|\vec{v}\times\vec{w}\|=\|\vec{v}\|\cdot\|\vec{w}\|\cdot\sin(\theta).\)

 

[RedSquirrel]

It is ridiculous to try to understand anything if you don't fully understand the definition.
Any two non-zero vectors form an angle. Suppose that \(\displaystyle \vec{v}~\&~\vec{w}\) are two non-zero vectors and
\(\displaystyle \theta\) is the angle between them. Then the cross-product \(\displaystyle \vec{v}\times\vec{w}\) is a vector that is perpendicular to both \(\displaystyle \vec{v}~\&~\vec{w}\) that has length \(\displaystyle \|\vec{v}\times\vec{w}\|=\|\vec{v}\|\cdot\|\vec{w}\|\cdot\sin(\theta).\)

Which way do \(\displaystyle \vec{v}~\&~\vec{w}\) face, or does it matter ?