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‫Welcome back.

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‫So I hope that you did the exercise and now to find the final key part for this total, we won't crossover

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‫to what you do.

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‫You cross out this role in this column, and that's your remaining two by two matrix, which is here.

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‫And then what you do, you take the determinant of it.

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‫And now you put the key unit vector here.

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‫But now it's positive, just like in the case, only J was negative.

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‫And so that's your final answer.

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‫And let's call it C, that's a key component of this tool cross product.

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‫And so the cross product, the one cross, the two equals you have a which was the eye component then

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‫minus B and then you had the J component and then plus C, which was the key component.

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‫And you know how to get your A, B and C from those remaining two by two matrices that you had.

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‫And don't forget in the J case you had a minus here.

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‫And so if you have numbers for these elements here, three elements for V one and three elements for

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‫V two, if you have numbers for them, then through this entire procedure that we had gone through,

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‫you will find some kind of numbers for A, B and C, let's say that A equals five and B equal six and

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‫C equals seven.

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‫Will then your cross product would be five ie minus six J and plus seven K or you can write it down

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‫like this if you want or if you want, you can draw it right here where these are your three components.

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‫And so you have five in the X direction, minus six in the wind direction and seven in the Z direction.

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‫And then the vector itself would look something like this, this green arrow that is composed of those

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‫three components.

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‫And minus six was this one here for the Y component.

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‫So this green vector here would be your V one, cross the two.

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‫Right.

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‫And a very important thing that you need to remember is that this vector that you get when you cross

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‫those two vectors, this green vector is perpendicular to V1 and V2.

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‫And so that's how you computed mathematically, that's the procedure that you get from linear algebra.

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‫And so in the next video, we're going to talk about some of the applications of cross products.

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‫Thank you very much.

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‫And see you there.