Respuesta :
The connection of curl in a cross product is a the curl is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.
According to the statement
we have to explain all about the connection with curl in the cross product.
So, For this purpose, we know that the
Cross product is the binary operation on two vectors in three dimensional space. It again results in a vector which is perpendicular to both the vectors. Cross product of two vectors is calculated by right hand rule.
Now, The connection of curl is a
Curl measures the twisting force a vector field applies to a point, and is measured with a vector perpendicular to the surface. Whenever you hear “perpendicular vector” start thinking “cross product”.
So, We take the “determinant” of this matrix:
[tex]\left[\begin{array}{ccc}i&j&k\\\frac{d}{dx} &\frac{d}{dy} &\frac{d}{dz} \\F_{x} &F_{y} &F_{z} \end{array}\right][/tex]
Then
Instead of multiplication, the interaction is taking a partial derivative. As before, the i vector component of curl is based on the vectors and derivatives in the j vector and k vector directions.
So, The connection of curl in a cross product is a the curl is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.
Learn more about cross product here
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