2. Demonstrate the following relationship involving the dot product and cross product (a) u. (V x W) = v. (w xu) = w. (u xv) (b) u. (u xv) = 0 (and explain geometrically why the result is zero) (c) (a × b) × (a × c) = [(a × b) · c]a (d) (a × b) · (c × d) = (a · c) (b · d) — (b · c) (a · d) (e) a × (b × c) + cx (a × b) + b × (c × a) = 0 (f) ||a+b|| ≤ ||a|| + ||b||
2. Demonstrate the following relationship involving the dot product and cross product (a) u. (V x W) = v. (w xu) = w. (u xv) (b) u. (u xv) = 0 (and explain geometrically why the result is zero) (c) (a × b) × (a × c) = [(a × b) · c]a (d) (a × b) · (c × d) = (a · c) (b · d) — (b · c) (a · d) (e) a × (b × c) + cx (a × b) + b × (c × a) = 0 (f) ||a+b|| ≤ ||a|| + ||b||
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve part a and c correctly and handwritten
![2. Demonstrate the following relationship involving the dot product and cross product
(a) u. (v xw) = v. (w × u) = w · (u x V)
(b) u. (u x v)
=
0
(and explain geometrically why the result is zero)
(c) (a × b) × (a × c) = [(a × b) · c]a
.
(d) (a × b). (c × d)
=
(a · c) (b · d) — (b · c) (a · d)
(e) a × (b × c) + cx (a × b) + b × (c × a) = 0
(f) ||a+b|| ≤ ||a|| + ||b||
(g) (a · b)² + ||a × b||² = ||a||²||b||².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84d305fc-e861-4250-8822-5e6a32ff70d4%2F320aca30-d02b-43ee-aadb-2ae737f0d695%2Fa9vckggb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Demonstrate the following relationship involving the dot product and cross product
(a) u. (v xw) = v. (w × u) = w · (u x V)
(b) u. (u x v)
=
0
(and explain geometrically why the result is zero)
(c) (a × b) × (a × c) = [(a × b) · c]a
.
(d) (a × b). (c × d)
=
(a · c) (b · d) — (b · c) (a · d)
(e) a × (b × c) + cx (a × b) + b × (c × a) = 0
(f) ||a+b|| ≤ ||a|| + ||b||
(g) (a · b)² + ||a × b||² = ||a||²||b||².
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