Answered: If a vector function F depends on both…

If a vector function F depends on both space coordinates (x, y, z) and time t, show that dF = (dr · ∇)F + (∂F/∂t)dt. Here, r = x i + y j + z k.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 72AP: Rectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6)...

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Question

If a vector function F depends on both space coordinates (x, y, z) and time t,
show that dF = (dr · ∇)F + (∂F/∂t)dt. Here, r = x i + y j + z k.

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