Hello, Ideasman!

Quote:

Anyone have an easy way for computing cross-products?

I came across:

$\displaystyle a \times b \;=\;\begin{bmatrix}0 & -a_3 & a_2 \\ a_3 & 0 &-a_1 \\ -a_2 & a_1& 0\end{bmatrix}\,\begin{bmatrix}b_1 \\ b_2 \\ b_3\end{bmatrix}$ . which seems very useful.

My book attempts to solve it by using determinants.

I prefer the determinant method.

I already know how to evaluate a 3-by-3 determinant.

. . Why would I want to memorize this new (and very strange) formula?

Quote:

Also, if we have two vectors, $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ in $\displaystyle R^2$, is $\displaystyle \vec{a} \times \vec{b}$ defined?

Not in $\displaystyle R^2$.

$\displaystyle \vec{a} \times \vec{b}$ is __perpendicular__ to both $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$. .It is automatically in $\displaystyle R^3$.

Quote:

If we have two vectors $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$,

I'm assuming those vectors are related to the $\displaystyle \vec{a} \times \vec{b}$

where their product is = 0, thus they're orthogonal?

Sorry, this makes no sense.

Are these are __any__ two vectors?

. . Then you mention their cross product . . . why?

"Their product is zero" . . . *What* product? .Dot product? .Cross product?

If their cross product is zero, the vectors are parallel.

If their dot product is zero, the vectors are orthogonal.

So what __exactly__ is your question?