‫Welcome back.
‫So I hope that you did the exercise and now to find the final key part for this total, we won't crossover
‫to what you do.
‫You cross out this role in this column, and that's your remaining two by two matrix, which is here.
‫And then what you do, you take the determinant of it.
‫And now you put the key unit vector here.
‫But now it's positive, just like in the case, only J was negative.
‫And so that's your final answer.
‫And let's call it C, that's a key component of this tool cross product.
‫And so the cross product, the one cross, the two equals you have a which was the eye component then
‫minus B and then you had the J component and then plus C, which was the key component.
‫And you know how to get your A, B and C from those remaining two by two matrices that you had.
‫And don't forget in the J case you had a minus here.
‫And so if you have numbers for these elements here, three elements for V one and three elements for
‫V two, if you have numbers for them, then through this entire procedure that we had gone through,
‫you will find some kind of numbers for A, B and C, let's say that A equals five and B equal six and
‫C equals seven.
‫Will then your cross product would be five ie minus six J and plus seven K or you can write it down
‫like this if you want or if you want, you can draw it right here where these are your three components.
‫And so you have five in the X direction, minus six in the wind direction and seven in the Z direction.
‫And then the vector itself would look something like this, this green arrow that is composed of those
‫three components.
‫And minus six was this one here for the Y component.
‫So this green vector here would be your V one, cross the two.
‫Right.
‫And a very important thing that you need to remember is that this vector that you get when you cross
‫those two vectors, this green vector is perpendicular to V1 and V2.
‫And so that's how you computed mathematically, that's the procedure that you get from linear algebra.
‫And so in the next video, we're going to talk about some of the applications of cross products.
‫Thank you very much.
‫And see you there.