If I understand correctly, you are going to use factor analysis on the 3 binary variables that are related to "interest in physics" and then create a binary variable from the factor scores. I don't think that will work. From the factor analysis you will get up to 3 sets of factor loadings for each variable, for which I don't see any way to derive a binary variable, and if you did find a way you would be discarding a lot of information by dichotomising.
An alternative approach would be to use a latent variable method, with one latent variable measured by the 3 related binary variables and then have the other variables predict the latent variable, this would be an example of a "Multiple Indicator, Multiple Cause" (MIMIC) model and would look like this:

where IntPhys is the latent variable for interest in physics, X1-X3 are the variables that measure interest in physics, and Z1-Z4 are the other variables that predict interest in physics. From this model you could investigate, for example, the strength of the regressions of IntPhys on Z1-Z4, whether these differ between groups (male and female for example), and whether the latent variable scores are different between groups.