Engineering Statics Problem in 3 dimensions

Can Matlab solve the summation of cross-products with unknowns? I'm working the problem below and would like to know how to solve this with Matlab instead of manually expanding the cross-product.

Unknowns: FED, FFC

Equation:

 {2k} FED{0.2673i 0.8018j 0.5345k} + {4k} FFC{ 0.6667i + 0.3333j 0.6667k} + {7k} { 490.5j} = 0

This simplifies to the following equation:

 ( 1.6036FED 1.3332FFC + 3433.5)i + (0.5334FED 2.6668FFC)j

Which can be solved by equating each vector to zero and solved simultaneously:

Mx = 0: .6036FED 1.3332FFC + 3433.5 = 0
My = 0: 0.5334FED 2.6668FFC = 0

I don't mind solving long-hand, since that's what I'd have to do on a test but I'd like to sharpen my Matlab skills too, if this can even be done in Matlab.

Cheers!

Jack

[Walter Roberson]

I do not understand your notation with {2k} and series of numbers in {}.

Are i and j and k intended to be the direction axes?

Answer 1

[Roger Stafford]

Yes, if you wish, you can solve your problem using matlab as follows:

   c1 = cross([0;0;2],[.2673;.8018;.5345]);
   c2 = cross([0;0;4],[.6667;.3333;.6667]);
   b = cross([0;0;7],[0;490.5;0]);
   X = [c1,c2]\(-b); % <-- Solve linear eqs.  (Edited)

The two elements in the vector X will be FED and FFC in that order. (You won’t get the same results as in your work by hand because you made some errors in the latter.)

The last line represents three equations with only two unknowns, in which case matlab seeks a least squares solution. However, since in this case the third equation is always satisfied with the given zeros, the X solution will be exact (to within rounding errors, of course.)

Note: I am not familiar with your notation for cross products.