Question

if r vector=xi+yj+zk then the value of curl (r n r vector)

Answer 1

Step-by-step explanation:

r = xi + yj + zk

To find:

Curl of r = xi + yj + zk

Solution:

curl r = V x r

j dy curl r = dz T3

dy curl r = dy

Here,

r₁ = x

r₂ = y

r3 = Z

curl r = (0-0)i + (0-0)j + (0-0)k

curl r = 0

So, curl r = 0

Answer 2

Answer:

curl $\textbf r = 0$

Step-by-step explanation:

Given $\textbf r=x\hat{i}+y\hat{j}+z\hat{k}$

$curl \textbf r =\det\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{\partial}{\partial x} &\frac{\partial}{\partial y} &\frac{\partial}{\partial z} \\x&y&z\end{array}\right]$

Using the formula for determinant

        $curl \textbf r =(\,\frac{\partial z}{\partial y}-\frac{\partial y}{\partial z})\, \hat{i}- (\,\frac{\partial z}{\partial x}-\frac{\partial x}{\partial z})\, \hat{j} + (\,\frac{\partial y}{\partial x}-\frac{\partial x}{\partial y})\,\hat{z}=0$

As the six partial derivatives are zero, the curl of a vector r is zero.