Question

The components of rotation for a three-dimensional flow field       

V = (y² + z²)$\hat{i}$+ (x² + z²)$\hat{j}$ + (x² + y²)$\hat{k}$ at (1, 2, 3) are

(a) $\omega _{x}$ = -1 rad/s ,   $\omega _{y}$ = 2 rad/s,  $\omega _{z}$ = -1 rad/s

(b) $\omega _{x}$ = -1 rad/s ,   $\omega _{y}$ = -1 rad/s,  $\omega _{z}$ = 2 rad/s

(c) $\omega _{x}$ = -2 rad/s ,   $\omega _{y}$ = -1 rad/s,  $\omega _{z}$ = -2 rad/s

(d) $\omega _{x}$ = 2 rad/s ,   $\omega _{y}$ = -2 rad/s,  $\omega _{z}$ = -1 rad/s