Answered: (a) P, Q and R are differentiable… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.1: Vector In R^n

Problem 28E

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Question

(a) P, Q and R are differentiable vector functions in R³ and is a scalar u. Show that
dQ
d[Px (QxR)] = Px[QxdR] + Px[du
du
du
dP
<R]+[d²XQXR)]
-x(QxR)
du
(b) If P = xe²i+sin(2xy)j + (3xy³ +1)k, Q = cos³ (z)i + 3xe³ j+xyzk and .
R=Sxy²zi + (x+ ye") j+x³zk, find [Px(QxR)]
at (1, 0, 0)
du

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