Question

Let $\vec{F}(x, y, z) = x \hat{i} + x y \hat{j} + \hat{k}$, then $\text{curl}(\vec{F})$ is

• A. $\hat{j} + x \hat{k}$
• B. $y \hat{k}$
• C. $\hat{i} + x \hat{j}$
• D. $x \hat{i} + x y \hat{j} + \hat{k}$

Hint:

Notice that $F_x$ and $F_y$ do not depend on $z$, and $F_z$ is constant. Thus all $z$-derivatives are zero, leaving only the $x,y$ derivative in the $\hat{k}$ component!

Answer 1

The Correct Option is B