Calculus 3: ERROR, WILL BE REPLACED Divergence and Curl (24 of 32) The Laplace Operator: Ex. 2

Left of the unit vectors. Video will be remade.

In this video I will find the Laplace operator of F=(y^2z^3)i+(2xyz^3)j+(3xy^2z^2)k.

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[chantianseng]

There are two mistakes.
1. Laplacian of a vector field turn up to be a vector field also.
2. Each of the vector field component has to proceed with second order differentiation wrt x, y, z axes.
The answer should be = (6 y^2 z + 2 z^3) i + (12 x y z) j + (6 x y^2 + 6 x z^2) k

[davidharispe]

That is definetely not the way the Laplacian Operator is applied to a vector field. This was also pointed by TS in another comment (and provided the right answer). You should apply the operator to each component of the vector field (as if each component is a scalar function) and then form a vector with the results.

Its a shame that this guy teaches things wrongly openly.

[jennieferadombire]

The final answer is suppose to be a vector, 6xy^2k

[georgewatko]

Michel, Should the final answer be a vector? so 6xy^2 (j)? rather than just 6xy^2??

[TANUJKUMARPandey]

Laplacian of a vector function is also a vector.

[joelleung]

I have no idea what he's saying but I appreciate such a smart guy sharing his knowledge with the world

[boburturimov]

Unfortunately it is not correct because we can't act Laplacian into vector field.