Question

. If r is the position vector of a point then div r is equal to *
(a) Zero
(b) 3
(c) 2
(d) None of the above
If you are able than do it!​

Answer 1

Answer:

c is the correct answer

Explanation:

Hope you are satisfied with the answer

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If $\vec{r}$ is the position vector of a point then div $\vec{r}$ is equal to

(a) Zero

(b) 3

(c) 2

(d) None of the above

EVALUATION

Here it is given that

$\vec{r}$ is the position vector of a point

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

Now div $\vec{r}$

= $\nabla .\vec{r}$

$\displaystyle \: = \bigg( \frac{ \partial}{ \partial x} \hat{i} + \frac{ \partial}{ \partial y} \hat{j} + \frac{ \partial}{ \partial z} \hat{k} \bigg).(x \hat{i} + y \hat{j} + z \hat{k})$

$\displaystyle \: = \frac{ \partial x}{ \partial x} + \frac{ \partial y}{ \partial y} + \frac{ \partial z}{ \partial z}$

$= 1 + 1 + 1$

$= 3$

FINAL ANSWER

Hence the correct option is (b) 3

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