Let $\mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { i } + x ^ { 2 } \mathbf { j } + y ^ { 2 } \mathbf { k }$ . Find the curl of F.
A) $2 y i$
B)$2 z j$

C)$2 x \mathbf { k }$
D)$2 y \mathbf { i } + 2 z \mathbf { j } + 2 x \mathbf { k }$
E)$2 x i$
F)$2 y j$
G)$2 z \mathbf { k }$
H)$2 x \mathbf { i } + 2 y \mathbf { j } + 2 z \mathbf { k }$

Question

Let $\mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { i } + x ^ { 2 } \mathbf { j } + y ^ { 2 } \mathbf { k }$ . Find the curl of F.
A) $2 y i$ 
B)$2 z j$

C)$2 x \mathbf { k }$
D)$2 y \mathbf { i } + 2 z \mathbf { j } + 2 x \mathbf { k }$
E)$2 x i$ 
F)$2 y j$
G)$2 z \mathbf { k }$ 
H)$2 x \mathbf { i } + 2 y \mathbf { j } + 2 z \mathbf { k }$

Quizplus · Accepted Answer

The curl of a vector field $\mathbf{F} = P\mathbf{i} + Q\mathbf{j} + R\mathbf{k}$ is given by $\nabla \times \mathbf{F} = \left( \frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z} \right)\mathbf{i} + \left( \frac{\partial P}{\partial z} - \frac{\partial R}{\partial x} \right)\mathbf{j} + \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right)\mathbf{k}$. For $\mathbf{F}(x, y, z) = z^2\mathbf{i} + x^2\mathbf{j} + y^2\mathbf{k}$, the curl is $2y\mathbf{i} + 2z\mathbf{j} + 2x\mathbf{k}$.

Let F(x,y,z)=z2i+x2j+y2k\mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { i } + x ^ { 2 } \mathbf { j } + y ^ { 2 } \mathbf { k }F(x,y,z)=z2i+x2j+y2k

Let $\mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { i } + x ^ { 2 } \mathbf { j } + y ^ { 2 } \mathbf { k }$