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a=2i+j, b=i-j+k

a=2i+j, b=i-j+k

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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12.3 EXERCISES 1. Which of the following expressions are meaningful? Which are meaningless? Explain. (a) (a b) c ● (c) a (b c) (e) a b + c ● ● ● (b) (a - b)c (d) a (b + c) ● (f) a (b + c) ● 2-10 Find a b. 2. a = (5,-2), b = (3, 4) 3. a = (1.5, 0.4), b = (-4, 6) 4. a = (6, -2, 3), b = (2, 5, -1) 5. a =(4, 1, 1), b = (6, -3, -8) 6. a = (p, -p, 2p), b = (2q, q, -q) 7. a = 2i+j, b=i-j+ k 8. a = 3i+2j - k, b = 4i + 5k 9. |a| = 7, |b|= 4, the angle between a and b is 30° 10. |a| = 80, b = 50, the angle between a and b is 37/4 sin nailsolo #RO-M $1 18 B * PI 11-12 If u is a unit vector, find u v and u w. 11. 12. entziq mi ziong dam 21:00 U W V 13. (a) Show that i ● (b) Show that i W j j k = k·i = 0. jj.kk ● i=j j = k·k = 1. 14. A street vendor sells a hamburgers, b hot dogs, and c soft drinks on a given day. He charges $4 for a hamburger, $2.50 for a hot dog, and $1 for a soft drink. If A = (a, b, c) and vodi naitw vino z p= (4, 2.5, 1), what is the meaning of the dot product A P? P 15-20 Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) 15. a = (4,3), b = (2, -1) 16. a = (-2,5), b = (5, 12)
Transcribed Image Text:12.3 EXERCISES 1. Which of the following expressions are meaningful? Which are meaningless? Explain. (a) (a b) c ● (c) a (b c) (e) a b + c ● ● ● (b) (a - b)c (d) a (b + c) ● (f) a (b + c) ● 2-10 Find a b. 2. a = (5,-2), b = (3, 4) 3. a = (1.5, 0.4), b = (-4, 6) 4. a = (6, -2, 3), b = (2, 5, -1) 5. a =(4, 1, 1), b = (6, -3, -8) 6. a = (p, -p, 2p), b = (2q, q, -q) 7. a = 2i+j, b=i-j+ k 8. a = 3i+2j - k, b = 4i + 5k 9. |a| = 7, |b|= 4, the angle between a and b is 30° 10. |a| = 80, b = 50, the angle between a and b is 37/4 sin nailsolo #RO-M $1 18 B * PI 11-12 If u is a unit vector, find u v and u w. 11. 12. entziq mi ziong dam 21:00 U W V 13. (a) Show that i ● (b) Show that i W j j k = k·i = 0. jj.kk ● i=j j = k·k = 1. 14. A street vendor sells a hamburgers, b hot dogs, and c soft drinks on a given day. He charges $4 for a hamburger, $2.50 for a hot dog, and $1 for a soft drink. If A = (a, b, c) and vodi naitw vino z p= (4, 2.5, 1), what is the meaning of the dot product A P? P 15-20 Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) 15. a = (4,3), b = (2, -1) 16. a = (-2,5), b = (5, 12)
Expert Solution
Step 1

The dot product, also known as the scalar product, is a binary operation that takes two vectors and returns a scalar (a single number). It is calculated as the product of the magnitudes of the two vectors and the cosine of the angle between them.

The dot product of two vectors a and b can also be calculated as the sum of the products of their corresponding components.

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