[Blindmath] Vector CrossMultiplication Question

[David Tseng]

Hey Rick, the notation is a little weird. i j k are usually used as
subscripts as are the numbers 1, 2, 3 in your examples.

The unit vectors in R^3 are:
(1, 0, 0) (0, 1, 0) (0, 0, 1).

Multiplying a vector with a scaler is just multiplying each component with
that scaler. In other words, the result is another vector.

Putting that back into the second formula, you can see you get back the
first form by distributing the scaler into each of the unit vectors above.
On Mon, Dec 12, 2016 at 4:08 AM Rick Thomas via Blindmath <
blindmath at nfbnet.org> wrote:

> Hi:
> I am reviewing Vector Cross Multiplication.
> One article claims that step 1 is to decompose any vector into Unit Form
> using (i,j,k)
> Others seem to use (i,j,k) only as component place holders in their
> equations unless they are assuming readers will know to do the unit
> decomposition before using their formulas.
> One article did not use (i,j,k) in their formula at all.
> Below are 2 solution formulas:
> Can you put into words whether decomposition needs to be performed to
> perform cross multiplication on 2 vectors prior to using them in the
> formula
> or show an example to explain a solution?
> Note: I use * to denote multiplication.
> First without (i,j,k)
> If the components for vectors A and B are known, then we can express the
> components of their cross product, C = A*B:
> Cx = (Ay*Bz - Az*By)
> Cy = (Az*Bx - Ax*Bz)
> Cz = (Ax*By - Ay*Bx)
> Second Article using (i,j,k)
> To take the cross product of two general vectors, we first decompose the
> vectors using the unit vectors i,j,k.
> Then proceed to distribute the cross product across the sums, using the
> rules to do the cross products between unit vectors.
> We can do this for arbitrary vectors
> u = u1, u2, u3)
>  and
> v = (v1, v2, v3)
>  to get a general formula:
> u = u1i + u2j + u3k
> v = v1i + v2j + v3k
> =
> (
> u1*v2 - u2*v1)k
> +
> (u3*v1 - u1*v3)j
> +
> (u2*v3 - u3*v2)i
> OK, so the above 2 methods look pretty similar but for the use of (i,j,k)
> Can you clear up this confusion for me either in words or by an example of
> 2
> vectors with component numbers not in unit form via a stepwise solution?
> I have not been able to figure this out in several days of googling.
> Are examples they give just specifying (i,j,k) just using them as place
> holders or do they actually calculate (i,j,k) and multiply the calculations
> by their values in the second example form?
> Rick USA
>
>
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