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6. Divergence and curl combinations (incl. identities) (a) Show that V. (fVg) = ƒV²g + Vf. Vg (b) Let f = zy + yx, v = (y, z, 4z - x)T, w = (y², z², x²) T. Find i. Vf and fVf at (3,4,0) T ii. V. (v x W) iii. curl(vx w) + curl(w x v)

6. Divergence and curl combinations (incl. identities) (a) Show that V. (fVg) = ƒV²g + Vf. Vg (b) Let f = zy + yx, v = (y, z, 4z - x)T, w = (y², z², x²) T. Find i. Vf and fVf at (3,4,0) T ii. V. (v x W) iii. curl(vx w) + curl(w x v)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Divergence and curl combinations (incl. identities) (a) Show that V. (fVg) = fV²g + Vf. Vg (b) Let f = zy + yx, v = (y, z, 4z - x)T, w = (y², z², x²) T. Find i. Vf and fVf at (3,4,0) T ii. V. (V x W) iii. curl(vx w) + curl(w x v)
Transcribed Image Text:6. Divergence and curl combinations (incl. identities) (a) Show that V. (fVg) = fV²g + Vf. Vg (b) Let f = zy + yx, v = (y, z, 4z - x)T, w = (y², z², x²) T. Find i. Vf and fVf at (3,4,0) T ii. V. (V x W) iii. curl(vx w) + curl(w x v)
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