How Do You Calculate the Moment of a Force About an Edge Using Determinants?

[ucflap]

Homework Statement

Hello guys, I have a physics class this session and I'm self-teaching myself most of the material. It's going not too bad so far but I have come across a form of solving I have not seen before and would like to understand how it works. I have the data and the answer, I just don't know how to get the answer from the equation. This is the last part of a problem I have to solve that deal with the moment of a force about an edge.

Homework Equations

For easier format, here is a picture:
http://unwantedcreations.com/img/physic_1.png
First line is λ of the edge
Second line are the coordinate of the point of application of force F
third line are the components x, y and z of the force F.

in case you don't get it at all, here is the problem and solution:
Problem
Solution

The Attempt at a Solution

Ok so I think I get where -25.363 come from, if you take 0.99228 * -1.8 * 14.2 it does make -25.363, but where does -10.5678 comes from? No idea.

Thank you for your time guys.

 

[tiny-tim]

hi ucflap!

Ok so I think I get where -25.363 come from, if you take 0.99228 * -1.8 * 14.2 it does make -25.363, but where does -10.5678 comes from? No idea.

it's 0.124035*6*14.2 …

to calculate a determinant, you multiply one element from each row and column, ie you zig-zag in every possible way

there are only two zig-zags that don't include a 0, and 0.124035*6*14.2 is one of them

(to see why it's minus, look up a book or wikipedia on determinants)