CLASSICAL DYNAMICS OF PARTICLES AND SYST
5th Edition
ISBN: 9780357670675
Author: Thornton
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 1, Problem 1.18P
Obtain the sine law of plane trigonometry by interpreting the product A × B and the alternate representation (A − B) × B.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
On a plane flat surface with "up" given as +y and "right" given as +x, we add two vectors. One of them has components (3, 4) and the other is (-1,-4). What is the length of the
resulting vector, and what direction is it pointing in?
The vector has length of 4 and it is in the positive x directon.
The vector has length of 12 and is pointing up and to the right at 45°.
The vector has length of 1 and is pointing up and to the left at 45°.
The vector has length of 2 in the positive x direction.
When three vectors are added graphically and form a closed
triangle, the largest enclosed angle between any two of the
vectors cannot be greater than
O 90°.
O 180°.
No maximum exists.
O 60°.
On a plane flat surface with "up" given as +y and "right" given as +x, we add two vectors. One of them has components (2, 4) and the other is (-1,-5). What is the length of the resulting vector, and what direction is it pointing in?
The vector has length of and is pointing up and to the right at 45°.
The vector has length of and is pointing down and to the right at 45°.
The vector has length of 1 and is pointing down and to the left at 45°.
The vector has length of 1 and is pointing up and to the left at 45°.
Chapter 1 Solutions
CLASSICAL DYNAMICS OF PARTICLES AND SYST
Ch. 1 - Prob. 1.1PCh. 1 - 1.2. Prove Equations 1.10 and 1.11 from...Ch. 1 - Prob. 1.3PCh. 1 - Show
(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1
Ch. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Consider a unit cube with one corner at the origin...Ch. 1 - Prob. 1.8PCh. 1 - For the two vectors
find
A − B and |A –...Ch. 1 - A particle moves in a plane elliptical orbit...
Ch. 1 - Prob. 1.11PCh. 1 - Let a, b, c be three constant vectors drawn from...Ch. 1 - X is an unknown vector satisfying the following...Ch. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - What surface is represented by r a = const, that...Ch. 1 - Obtain the cosine law of plane trigonometry by...Ch. 1 - Obtain the sine law of plane trigonometry by...Ch. 1 - Prob. 1.19PCh. 1 - 1-20. Show that
Ch. 1 - Show (see also Problem 1–11) that
Ch. 1 - Prob. 1.22PCh. 1 - Use the εijk notation and derive the identity
(A ×...Ch. 1 - Prob. 1.24PCh. 1 - Find the components of the acceleration vector a...Ch. 1 - Prob. 1.26PCh. 1 - If r and are both explicit functions of time,...Ch. 1 - Show that
Ch. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Show that
(a)
(b)
(c)
Ch. 1 - Show that (2arr+2brr)dt=ar2+br2+const. where r is...Ch. 1 - Show that (rrrrr2)dt=rr+C where C is a constant...Ch. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - A plane passes through the three points (x, y, z)...Ch. 1 - For what values of a are the vectors A = 2ai − 2j...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- What surface is represented by r a = const, that is described if a is a vector of constant magnitude and direction from the origin and r is the position vector to the point P(x1, x2, x3) on the surface?arrow_forwardTwo points in the xy plane have Cartesian coordinates (2.00, 4.00) m and (3.00, 3.00) m. Determine (a) the distance between these points and (b) their polar coordinates.arrow_forwardFigure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.arrow_forward
- Rectangular coordinates of a point are given by (2, y) and its polar coordinates are given by (r, π/6) . Find y and r.arrow_forwardMathematically, for two vectors A and B of any magnitude, the cross product of both, i.e. AxB = given by: a) |A||B|sinØ b) |A||B| c) |A||B|cosØ d) |A||B|sin(180°+Ø)arrow_forwardStep 1 Rewrite the original integral Therefore, let du a² + u² (²) dt as + 16 = arctan(y) to Step 2 Use the following integration formula for the inverse trigonometric functions. 1.20 t (27²2² +42 (2) ot = (- t 1 + X X 4 2 (2) dt arctant arctan tan()+c 4 ✓)) + Carrow_forward
- Needs Complete typed solution with 100 % accuracy.arrow_forwardLet vector A point from the origin into the second quadrant of the xy plane and vector B point from the origin into the fourth quadrant. The vector B −A must be in which quadrant?arrow_forwardDesign a 4-bit binary magnitude comparator and write the expressions for Y1(A>B), Y2 (A=B) and Y3 (A<B).arrow_forward
- Please answer A.3arrow_forwardGiven the 3-dimensional vectors : A = i (xy) + j (2yz) + k (3zx) B = i (yz) + j (2zx) + k (3xy). Determine the magnitude of the vector sum |A + B| at coordinates (3,2,1).arrow_forwardLet 7 be the vector (5,6,-7) and the vector (-0.625, 0.469, 0.625). What is × Â ?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Introduction to Vectors and Their Operations; Author: Professor Dave Explains;https://www.youtube.com/watch?v=KBSCMTYaH1s;License: Standard YouTube License, CC-BY