2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v xw) = v. (w xu) = 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). (cx d) (a · c) (b · d) — (b. c) (a ·d) (e) ax (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.
2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v xw) = v. (w xu) = 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). (cx d) (a · c) (b · d) — (b. c) (a ·d) (e) ax (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.
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 parts d and e 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%2F218bce4a-09f0-47fe-86be-0afd68e6cba3%2Fui0ejfx_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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