Explanation Establish a position vector for points A , B , and C . The coordinates are: point A ( 0 , − 2 , 0 ) m , point B ( 0 , 0 , 0 ) m , and point C ( 3 , 4 , − 1 ) m. Express the position vector r in the direction of BA . r B A = ( x A − x B ) i + ( y A − y B ) j + ( z A − z B ) k (I) Here, the coordinates of A and B are x A , x B , y A , y B , z A , and z B , respectively. Express the position vector r in the direction of BC . r B C = ( x C − x B ) i + ( y C − y B ) j + ( z C − z B ) k (II) Here, the coordinates of B and C are x B , x C , y B , y C , z B , and z C , respectively. Express the magnitude of the direction of BA . r B A = ( x A − x B ) 2 + ( y A − y B ) 2 + ( z A − z B ) 2 (III) Express the magnitude of the direction of BC . r B C = ( x C − x B ) 2 + ( y C − y B ) 2 + ( z C − z B ) 2 (IV) Determine the unit vector of BA . u B A = ( r B A r B A ) (V) Here, the position vector in the direction of BA is r B A , and the magnitude of the position vector in the direction of BA is r B A . Determine the unit vector of BC . u B C = ( r B C r B C ) (VI) Here, the position vector in the direction of BC is r B C , and the magnitude of the position vector in the direction of BC is r B C . Apply the dot product to find the angle between two cables. u B A ⋅ u B C = cos θ θ = cos − 1 ( u B A ⋅ u B C ) (VII) Conclusion: Substitute 0 m for x A , 2 m for y A , 0 m for z A , 0 m for x B , 0 m for y B , and 0 m for z B in Equation (I). r B A = ( 0 − 0 ) i + ( − 2 − 0 ) j + ( 0 − 0 ) k = ( − 2 j ) m Substitute 3 m for x C , 4 m for y C , 1 m for z C , 0 m for x B , 0 m for y B , and 0 m for z B in Equation (II)

Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

14th Edition

ISBN: 9780134229287

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

Videos

Question

Chapter 2.9, Problem 128P

To determine

The angle θ between BA and BC.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.9, Problem 127P

Chapter 2.9, Problem 129P

Students have asked these similar questions

Which one of the following is the most common polymer type in fiber-reinforced polymer composites? thermosets thermoplastics elastomers none of the above

A pattern for a product is larger than the actual finished part. True or False

In the lost foam process, the pattern doesn’t need to be removed from the mold. True or False

Chapter 2 Solutions

Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

Ch. 2.3 - Then establish the triangle rule, where FR = F1 +...Ch. 2.3 - Then establish the triangle rule to show FR = FU +...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 this force into components acting along...Ch. 2.3 - along the v axis. Prob. F2-6 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.

The angle θ between BA and BC .

Solution Summary: The author determines the angle theta between BA and BC. Establish a position vector for points A, B, and C.

Concept explainers

Videos

The angle θ between BA and BC.

Want to see the full answer?

Chapter 2 Solutions