Possible Error in "distance between planes " video on linear algebra.

Hi kaibarreraera,

If you break the j component up into a smaller matrix, you get the following:

  | 2  1 |   =   (2)(1) - (4)(1) = -2
  | 4  1 | 

The j component of the cross product is always the negative value of the smaller matrix determinant, so the final result is -(-2) = +2.

I hope this helps! Please let me know if you have any additional questions!

I think I understand now. Perhaps in the previous video he was strictly adding each determinant meaning the j component would have to be (4)(1) - (2)(1) = +2 to correct for the sign. However if we are following the structure of +i -j +k instead of +i +j +k like the above, we would have to use (2)(1) - (4)(1). Thank you!