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
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dbe3aca-3bf2-4221-bb74-64e96a02685e%2F281e3465-93ce-4400-b094-267661452a6e%2Fcvpas3_processed.jpeg&w=3840&q=75)
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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