Explanation Given information: The three vectors A , B , and D respectively. Calculation: Use the Cartesian vector formulation to prove A ⋅ ( B + D ) = ( A ⋅ B ) + ( A ⋅ D ) . Use the formulas of Cartesian unit dot vectors. i ⋅ j = i ⋅ k = j ⋅ k = 0 i ⋅ i = j ⋅ j = k ⋅ k = 1 Conclusion: Write the Cartesian vector form of A ⋅ ( B + D ) . A ⋅ ( B + D ) = ( A x i + A y j + A z k ) ⋅ [ ( B x + D x ) i + ( B y +

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 2.9, Problem 71P

To determine

Show that A⋅(B+D)=(A⋅B)+(A⋅D).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.9, Problem 31FP

Chapter 2.9, Problem 72P

Students have asked these similar questions

Complete the following problems. Show your work/calculations, save as.pdf and upload to the assignment in Blackboard. missing information to present a completed program. (Hint: You may have to look up geometry for the center drill and standard 0.5000 in twist drill to know the required depth to drill). 1. What are the x and y dimensions for the center position of holes 1,2, and 3 in the part shown in Figure 26.2 (below)? 6.0000 Zero reference point 7118 1.0005 1.0000 1.252 Bore 6.0000 .7118 Cbore 0.2180 deep (3 holes) 2.6563 1.9445 Figure 26.2 026022 (8lot and Drill Part) (Setup Instructions--- (UNITS: Inches (WORKPIECE NAT'L SAE 1020 STEEL (Workpiece: 3.25 x 2.00 x0.75 in. Plate (PRZ Location 054: ' XY 0.0 - Upper Left of Fixture TOP OF PART 2-0 (Tool List ( T02 0.500 IN 4 FLUTE FLAT END MILL #4 CENTER DRILL Dashed line indicates- corner of original stock ( T04 T02 3.000 diam. slot 0.3000 deep. 0.3000 wide Intended toolpath-tangent- arc entry and exit sized to programmer's judgment…

A program to make the part depicted in Figure 26.A has been created, presented in figure 26.B, but some information still needs to be filled in. Compute the tool locations, depths, and other missing information to present a completed program. (Hint: You may have to look up geometry for the center drill and standard 0.5000 in twist drill to know the required depth to drill).

We consider a laminar flow induced by an impulsively started infinite flat plate. The y-axis is normal to the plate. The x- and z-axes form a plane parallel to the plate. The plate is defined by y = 0. For time t <0, the plate and the flow are at rest. For t≥0, the velocity of the plate is parallel to the 2-coordinate; its value is constant and equal to uw. At infinity, the flow is at rest. The flow induced by the motion of the plate is independent of z. (a) From the continuity equation, show that v=0 everywhere in the flow and the resulting momentum equation is მu Ət Note that this equation has the form of a diffusion equation (the same form as the heat equation). (b) We introduce the new variables T, Y and U such that T=kt, Y=k/2y, U = u where k is an arbitrary constant. In the new system of variables, the solution is U(Y,T). The solution U(Y,T) is expressed by a function of Y and T and the solution u(y, t) is expressed by a function of y and t. Show that the functions are identical.…

Chapter 2 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Determine the magnitude of the resultant force....Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - Resolve the force into components acting along...Ch. 2.3 - Prob. 6FP Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Show that A ⋅ ( B + D ) = ( A ⋅ B ) + ( A ⋅ D ) .

Solution Summary: The author demonstrates the Cartesian vector form of A, B and D.

Videos

Show that A⋅(B+D)=(A⋅B)+(A⋅D).

Want to see the full answer?

Chapter 2 Solutions