Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 1.12P
Let a, b, c be three constant vectors drawn from the origin to the points A, B C. What is the distance from the origin to the plane defined by the points A, B C? What is the area of the triangle ABC?
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a. The vector from the origin to point A is given as (6,–2,-4), and
the unit vector directed from the origin toward point B is
(2,-2,1)/3. If points A and B are ten units apart, find the
coordinates of point B.
Find the area of the triangle determined by the points P, Q, and R. Find a unit vector perpendicular to plane PQR.
Р(- 1,1, - 2), Q(-2,0,1), R(0, -2, - 1)
K is a vector field and V is a scalar field. The divergence of K is equal V; that is V = V.K.
Evaluate V in cylindrical coordinates and determine V at the point (r, p, z)= (25, 45°, 5) if
r cos p
Z
K = r cos² or +
Note: Please write the answer NUMERICALLY.
Answer:
-- 3z sin p2
Chapter 1 Solutions
Classical Dynamics of Particles and Systems
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...
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