Cross Product Fun: Deriving Statement 2 from Statement 1

[jesuslovesu]

Homework Statement

1 $$(H_1 - H_2) \times \hat n = J_s$$
2 $$(H_1t - H_2t) = \hat n \times J_s$$

How does one get from the first statement to the second statement?

3 $$H_{1t} - H_{2t} = J_s$$

This is causing an interesting problem when I plug in numbers, I would have just left it with statement (3) but if I do I get something completely different. My book gives (2) but doesn't explain how it derives it.

 

[Dick]

If the 't' means 'tangential' part use ax(bxc)=b(a.c)-c(a.b). The H part becomes H minus the normal component of H.