How to solve cross products in physics problems?

[uchicago2012]

Homework Statement

I'm solving a physics problem using cross products and I think I might be doing the cross products wrong

Homework Equations

I'm using the formula:
a cross b = (a₂b₃- a₃b₂)x + (a₃b₁- a₁b₃)y + (a₁b₂- a₂b₁)z
where a₁ = a_x, a₂ = a_y, a₃ = a_z, etc.
I don't know if this formula should be used on matrices like these, esp. the second cross product since its not 3 * 3 or 2 * 2 matrix, which I'm pretty sure is all that the formula is intended for. I had to get off wikipedia because my physics book doesn't go into how to solve cross products and I don't have any algebra books around.

The Attempt at a Solution

The cross products are:
(2.5x - 4.3y + 5.1z) cross (-2.4x + 8.0y - 2.6z)
and
(2.5x - 4.3y + 5.1z) cross (10x + 14y)

I got

(-29.62x - 5.74y + 9.68z) for the first one
and
(-71.4x +51y + 78z) for the second one

 

[cepheid]

I don't know if this formula should be used on matrices like these, esp. the second cross product since its not 3 * 3 or 2 * 2 matrix, which I'm pretty sure is all that the formula is intended for.

What matrices? What 3x3 and 2x2? What are you talking about?
This is the formula for the cross product of two vectors, each of which has 3 components.

The Attempt at a Solution

The cross products are:
(2.5x - 4.3y + 5.1z) cross (-2.4x + 8.0y - 2.6z)
and
(2.5x - 4.3y + 5.1z) cross (10x + 14y)

I got

(-29.62x - 5.74y + 9.68z) for the first one
and
(-71.4x +51y + 78z) for the second one

The first one that you did checks out fine for me.

 

[Twoism]

The second one should be (-71.4x + 51y 78z). So yes, you got them both right.