Question

What is curl of the vector field $2x^{2}y\hat{i}+5z^2\hat{j}-4yz\hat{k}?$

• A. $-14z\hat{i}-2x^2\hat{k}$
• B. $6z\hat{i}+4x\hat{j}-2x^2\hat{k}$
• C. $6z\hat{i}+8xy\hat{j}+2x^{2}y\hat{k}$
• D. $-14z\hat{i}+6y\hat{j}+2x^2\hat{k}$

Answer 1

The correct option is A $-14z\hat{i}-2x^2\hat{k}$

Curl of the vector field = $\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ \frac{\partial }{\partial x}& \frac{\partial }{\partial y}& \frac{\partial }{\partial z}\\ 2x^{2}y& 5z^2& -4yz\end{array}\right|$
= $\hat{i}$(-4z-10z)-$\hat{j}$(0-0) +$\hat{k}$ $(0-2x^2$)
= $-14z\hat{i}-2x^2\hat{k}$