Show that if F = xi+yj+zk, then VXF=0.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Show that if F = xi+yj + zk, then VXF=0.
The curl of a vector field F = Mi+Nj + Pk is as follows.
ap ƏN
?M
ap
dy dz
dz
?x
Use the formula above to find the curl of F=xi+yj + zk.
curl F = VXF=
VxF =
V x (xi+yj+zk)
dz dy
= - i+
dy dz
=
i+
İ+
dx dz
dz ?x
+
k
j+
dy ax
?x ду
ƏN
ax
k
ƏM
ду
Transcribed Image Text:Show that if F = xi+yj + zk, then VXF=0. The curl of a vector field F = Mi+Nj + Pk is as follows. ap ƏN ?M ap dy dz dz ?x Use the formula above to find the curl of F=xi+yj + zk. curl F = VXF= VxF = V x (xi+yj+zk) dz dy = - i+ dy dz = i+ İ+ dx dz dz ?x + k j+ dy ax ?x ду ƏN ax k ƏM ду
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