Improved the explanation, looking for suggestions.
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Computes the [[cross product|https://en.wikipedia.org/wiki/Cross_product]] of the two input [[vector]]s. |
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The Cross Product calculates the cross product of the two input vectors, and outputs another vector. |
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| 3 | Let's say that Vector C is the cross product of these two vectors:\ |
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| 4 | **Vector A:** (Ax, Ay, Az)\ |
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| 5 | **Vector B:** (Bx, By, Bz) |
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| 3 | [[/uploads/Cross Product.png]] |
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| 6 | 4 | |
| 7 | If we split the components, the formula to find the cross product is:\ |
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| 8 | **Cx:** (Ay×Bz)-(Az×By)\ |
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| 9 | **Cy:** (Az×Bx)-(Ax×Bz)\ |
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| 10 | **Cz:** (Ax×By)-(Ay×Bx) |
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| 5 | ## Details |
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| 11 | 6 | |
| 12 | The cross product is used to find a vector that is perpendicular to to both vectors. |
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| 7 | The Cross Product is a way of multiplying two vectors together. |
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| 8 | We can calculate the Cross Product of two vectors this way, let's say that the cross product of A and B is vector C: |
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| 13 | 9 | |
| 14 | [[/uploads/Cross Product.png]] |
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| 0 | Cx = Ay × Bx - Az × By |
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| 1 | Cy = Az × Bx - Ax × Bz |
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| 2 | Cz = Ax × By - Ay × Bx |
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| 4 | It outputs the vector that is perpendicular to both input vectors (or the plane spanned by those two vectors). |
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| 6 | The length of that vector is equal to the area of the parallelogram formed by those two input vectors (each vector gives a pair of parallel sides). Not that common for this knowledge to be used, you would often use the vector for it's direction and not it's length. |