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Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W): = V. · (w xu) = w (ux v) (b) u. (u xv) = 0 (c) (ax b) x (a x c) = [(a × b) c]a (and explain geometrically why the result is zero)

Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W): = V. · (w xu) = w (ux v) (b) u. (u xv) = 0 (c) (ax b) x (a x c) = [(a × b) c]a (and explain geometrically why the result is zero)

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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Please solve first 3 parts correctly and handwritten
2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W) = v. (w x u) = w. . (ux v) (b) u. (ux v) = 0 (c) (a × b) × (a × c) = [(a × b) · c]a (d) (a × b). (cx d) = (a · c) (b · d) (b. c) (a.d) (and explain geometrically why the result is zero)
Transcribed Image Text:2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W) = v. (w x u) = w. . (ux v) (b) u. (ux v) = 0 (c) (a × b) × (a × c) = [(a × b) · c]a (d) (a × b). (cx d) = (a · c) (b · d) (b. c) (a.d) (and explain geometrically why the result is zero)
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