Compute curl F for F = (x - z) i + (y - x) j + (z - y) k.
A) - i + j - k
B) i + j + k
C) - i + j + k
D) i - j
E) 0

Question

Quizplus · Accepted Answer

The curl of a vector field F = (P, Q, R) is given by ∇ × F = (∂R/∂y - ∂Q/∂z) i + (∂P/∂z - ∂R/∂x) j + (∂Q/∂x - ∂P/∂y) k. For F = (x - z, y - x, z - y), we have P = x - z, Q = y - x, R = z - y. Calculating each component: ∂R/∂y - ∂Q/∂z = -1 - 0 = -1, ∂P/∂z - ∂R/∂x = -1 - 0 = -1, ∂Q/∂x - ∂P/∂y = -1 - 0 = -1. Thus, curl F = -i + j - k.

Compute Curl F for F = (X - Z) I