(a) P, Q and R are differentiable vector functions in R³ and is a scalar u. Show that dQ du [PX (QXR)] = Px[Qx dR] + Px[dexR]+[d²x (0×R)] -×(Q×R) du du du

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(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
Transcribed Image Text:(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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