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Demonstrate the following relationships involving the determinate (a) Vector cross product (b) Triple scalar product (c) Permutation symbol a x b = aibj€ijkêk Eijk = a1 a2 a3 a. (bx c) = abjck Eijk =b₁ b₂ b3 C1 C2 C3 dil di2 di3 81 82 83 Sk1 Sk2 k3 kl ê ê2 e3 1 =a1 a2 a3 b₁ b2 b3 = Si1 j1 Skl Si2 j2 Sk2 бiз бiз бкз i3

Demonstrate the following relationships involving the determinate (a) Vector cross product (b) Triple scalar product (c) Permutation symbol a x b = aibj€ijkêk Eijk = a1 a2 a3 a. (bx c) = abjck Eijk =b₁ b₂ b3 C1 C2 C3 dil di2 di3 81 82 83 Sk1 Sk2 k3 kl ê ê2 e3 1 =a1 a2 a3 b₁ b2 b3 = Si1 j1 Skl Si2 j2 Sk2 бiз бiз бкз i3

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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3. Demonstrate the following relationships involving the determinate (a) Vector cross product (b) Triple scalar product (c) Permutation symbol a x b = a;bj€ijkek a · (b x c) = ajbjck€ijk Eijk Si1 2 3 бj1 бj2 бj3 бki бkz бk3 = ê ê2 e3 a1 a2 аз b1b2b3 = 01 a2 a3 b1 b2 b3 C1 C2 C3 Si1 Sj1 Sk1 Si2 j2 бiз бiз бk3 k2
Transcribed Image Text:3. Demonstrate the following relationships involving the determinate (a) Vector cross product (b) Triple scalar product (c) Permutation symbol a x b = a;bj€ijkek a · (b x c) = ajbjck€ijk Eijk Si1 2 3 бj1 бj2 бj3 бki бkz бk3 = ê ê2 e3 a1 a2 аз b1b2b3 = 01 a2 a3 b1 b2 b3 C1 C2 C3 Si1 Sj1 Sk1 Si2 j2 бiз бiз бk3 k2
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