Try the fastest way to create flashcards
Question

# In given problem, find div $\mathbf{F}$ and curl $\mathbf{F}$.$\mathbf{F}(x, y, z)=(y+z) \mathbf{i}+(x+z) \mathbf{j}+(x+y) \mathbf{k}$

Solution

Verified
Step 1
1 of 3

\begin{align*} \nabla\cdot\mathbf{F} &= \left\langle\dfrac{\partial}{\partial x},\dfrac{\partial}{\partial y},\dfrac{\partial}{\partial z}\right\rangle \cdot \left\langle M,N,P\right\rangle\\ &= \dfrac{\partial M}{\partial x} + \dfrac{\partial N}{\partial y} + \dfrac{\partial P}{\partial z}\\ &=\dfrac{\partial}{\partial x}(y+z)+\dfrac{\partial}{\partial y}(x+z)+\dfrac{\partial}{\partial z}(x+y)\\ &=0+0+0\\ &=0 \end{align*}

Calculate the divergence of $\mathbf{F}$.

## Recommended textbook solutions #### Calculus

9th EditionISBN: 9780131429246Dale Varberg, Edwin J. Purcell, Steve E. Rigdon
6,552 solutions #### Thomas' Calculus

14th EditionISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,142 solutions #### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (6 more)James Stewart
11,084 solutions #### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927 (1 more)Daniel K. Clegg, James Stewart, Saleem Watson
11,050 solutions