Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 3, Problem 12PQ
To determine
Show that vector addition is associative.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
(a) Find the scalar products î · î, ĵ· ĵ, and k · Ê.
(b) Find î · ĵ, ĵ · k, and k · î
(c) Use the distributive law to multiply out the scalar product of two arbitrary vectors Ã
Axî + Ayî + A¸k and B
Equation 6.4.
Bxî + Byĵ + Bzk, and use the results of (a) and (b) to verify
Problem 2.16 The divergence of a vector F is given by
1 a(pF,) , 13F, , ƏF,
V.F =
+
az
Evaluate V · F for
F(p.0.2) = pp+z sin ø4+Jpzk.
Answer: 2+zcoso/p+VP/z.
Prove that for any vector u, u = (u e,)e, +(u ·e, )e, + (u e,)e,. [Hint: write u in
component form.]
Find the projection of the vector u e, -2e, +e, on the vector
2.
3.
v = 4e, - 4e, + 7e,.
Chapter 3 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 3.1 - The three vectors A,B and C in Figure 3.7 all have...Ch. 3.1 - Prob. 3.2CECh. 3.1 - a. You wish to represent free-fall acceleration...Ch. 3.2 - Prob. 3.4CECh. 3.3 - Prob. 3.5CECh. 3 - A velocity vector has a magnitude of 720 m/s. Two...Ch. 3 - A young boy throws a baseball through a window. a....Ch. 3 - Prob. 3PQCh. 3 - Prob. 4PQCh. 3 - Vector A, with a magnitude of 18 units, points in...
Ch. 3 - Prob. 6PQCh. 3 - Prob. 7PQCh. 3 - The layout of the town of Popperville is a...Ch. 3 - Prob. 9PQCh. 3 - Prob. 10PQCh. 3 - Prob. 11PQCh. 3 - Prob. 12PQCh. 3 - In Chapter 5, you will study a very important...Ch. 3 - Refer to the situation described in Problem 14....Ch. 3 - Vector A has a magnitude of 4.50 m and makes an...Ch. 3 - Miguel, an Ultimate Frisbee player, is running...Ch. 3 - A baseball diamond consists of four plates...Ch. 3 - Prob. 19PQCh. 3 - Prob. 20PQCh. 3 - Two aircraft approaching an aircraft carrier are...Ch. 3 - Prob. 22PQCh. 3 - A truck driver delivering office supplies downtown...Ch. 3 - Prob. 24PQCh. 3 - Carolyn rides her bike 40.0 south of west for 5.40...Ch. 3 - Prob. 26PQCh. 3 - Prob. 27PQCh. 3 - Prob. 28PQCh. 3 - Prob. 29PQCh. 3 - Prob. 30PQCh. 3 - Prob. 31PQCh. 3 - Prob. 32PQCh. 3 - Prob. 33PQCh. 3 - Prob. 34PQCh. 3 - A firecracker explodes into four equal pieces...Ch. 3 - Prob. 36PQCh. 3 - Prob. 37PQCh. 3 - Prob. 38PQCh. 3 - Prob. 39PQCh. 3 - Figure P3.40 shows a map of Grand Canyon National...Ch. 3 - Prob. 41PQCh. 3 - The same vectors that are shown in Figure P3.6 are...Ch. 3 - A supertanker begins in Homer, Alaska, sails 125...Ch. 3 - A Three vectors are shown in Figure P3.44, but...Ch. 3 - A vector A=(5.20i3.70j) m and a vector...Ch. 3 - Prob. 46PQCh. 3 - Prob. 47PQCh. 3 - Prob. 48PQCh. 3 - An airplane leaves city A and flies a distance d1...Ch. 3 - An aircraft undergoes two displacements. If the...Ch. 3 - The resultant vector R=2AB2C has zero magnitude....Ch. 3 - A Three vectors all have the same magnitude. The...Ch. 3 - The two-dimensional vectors A and B both have...Ch. 3 - Prob. 54PQCh. 3 - Two birds begin next to each other and then fly...Ch. 3 - Prob. 56PQCh. 3 - General Problems 57. G A spider undergoes the...Ch. 3 - Peter throws a baseball through a houses window....Ch. 3 - Prob. 59PQCh. 3 - Prob. 60PQCh. 3 - Prob. 61PQCh. 3 - A glider aircraft initially traveling due west at...Ch. 3 - What are the magnitude and direction of a vector...Ch. 3 - Prob. 64PQCh. 3 - Prob. 65PQCh. 3 - Prob. 66PQCh. 3 - Prob. 67PQCh. 3 - Prob. 68PQCh. 3 - Prob. 69PQCh. 3 - Prob. 70PQCh. 3 - Vector F is proportional to vector A such that...Ch. 3 - Prob. 72PQCh. 3 - Prob. 73PQCh. 3 - Problems 74 and 75 are paired. 74. N A classroom...Ch. 3 - Prob. 75PQ
Knowledge Booster
Similar questions
- The vectors from the origin to the points A, B, and C are i + j, 3i + k, and 4i – 3j – 4k, respectively. Show that .4BC is a right triangle, and find its area.arrow_forwardExpress the ff. as a single 2 × 2 matrix. exp (it)arrow_forwardx = 2uv +3 y = vw z = wu. #3. Find the gradient vector field Vf of the function f (x, y,z) = x²y +z sinx. Evaluate the line integralarrow_forward
- Answer with complete solution, and write the given vectors in terms of its components and the corresponding unit vector and then verify the initial result by adding these vectors algebraicallyarrow_forwardWhat 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_forwardConsider the points K(−1, 0, 7) and M(1, −2, 5), the vector MN = <1, 4, −3>, and the line L with symmetric equations 16 − x = y − 18 = z + 11.1) Determine the coordinates of point N.2) Write the vector KM in terms of its components. Please write the answer on paper, do not just type the answer and solutions.arrow_forward
- Find a vector of length 2 in the opposite direction of the displacement from P,(-2,3,5) to P,(3,5,- 2). Express your answer in component form (x, y.arrow_forwardGiven the vectors A = -5i - 3j - 8k ; B = 4i - 2j + 3k ; C = 10i -12j - 8k a. Find A x B b. Evaluate the mixed triple products A . (B x C) c. Find : A x (A x B)arrow_forwardI know that E is the correct answer. I understand why statement I is correct, but why is statement 2 wrong and statement 3 right?arrow_forward
- Prove the Jacobi identity: A × (B × C) + B × (C × A) + C × (A × B) = 0. Hint:Expand each triple product as in equations (3.8) and (3.9).arrow_forwardAn alternative line definition Given a fxed point P,(xo- Yo) and a nonzero vector n = (a, b), the set of points P(x, y) for which PP is orthogonal to n is a line e (see figure). The vector n is called a normal vector or a vector normal to e. yA n = (a, b) P(x, y) Suppose a line is normal to n = (5, 3). What is the slope of the line?arrow_forwardTwo particles, each of mass m, are connected by a light inflexible string of length l. The string passes through a small smooth hole in the centre of a smooth horizontal table, so that one particle is below the table and the other can move on the surface of the table. Take the origin of the (plane) polar coordinates to be the hole, and describe the height of the lower particle by the coordinate z, measured downwards from the table surface. i. sketch all forces acting on each mass ii. explain how we get the following equation for the total energyarrow_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
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning