a) Show that if u, v, and w are differentiable vector functions of t, then d du V X w +u - dt dv dw (u ·v × w) dt X w + u•v x - dt dt b) Show that

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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a) Show that if u, v, and w are differentiable vector functions of t, then
d
du
dv
dw
(u·v x w)
dt
v x w + u. xw+u•vx·
dt
dt
dt
b) Show that
dr d'r
dt * dt?
(dr d³r\
= r:
dt
d
dt
dt3
Transcribed Image Text:a) Show that if u, v, and w are differentiable vector functions of t, then d du dv dw (u·v x w) dt v x w + u. xw+u•vx· dt dt dt b) Show that dr d'r dt * dt? (dr d³r\ = r: dt d dt dt3
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