Question

The curl of vector field F =x’yi + xyz] + z’yk at the point (0,1, 2) is​

Answer 1

Answer:

playing like my answer pls

Answer 2

Concept:

We need to recall the concept of curl of  a vector field to answer this question.

Curl of a vector field F(x,y,z) = Xi+Yj+Zk is denoted by curl F.

Defined as: curl F =     $\begin{vmatrix} i & j & k\\ \frac{d}{dx} & \frac{d}{dy}&\frac{d}{dz} \\ X &Y &Z \end{vmatrix}$

Given:

The vector field F = xy i +xyz j +zy k

To find:

The curl of vector field at point (0,1,2).

Solution:

On Comparing the given vector field with

   F(x,y,z) = Xi+Yj+Zk

we get, X = xy

             Y = xyz

             Z = zy

Curl of F is given by :

Curl F =  $\begin{vmatrix} i & j & k\\ \frac{d}{dx} & \frac{d}{dy}&\frac{d}{dz} \\xy&xyz&zy\end{vmatrix}$

          = (z-xy) i - (0-0) j + (yz- x) k

          =  (z-xy) i + 0 j + (yz- x) k

At point (0,1,2),

Curl F = (2-0×1 ) i +0 j + (1×2 -0) k

          = 2 i +0 j + 2k

Hence, curl of the vector field at point (0,1,2) is given  by : 2 i +0 j + 2k