Explanation Consider that if A → = A x i ^ + A y j ^ + A z k ^ then − A → = ( − A x ) i ^ + ( − A y ) j ^ + ( − A z ) k ^ , if B → = B x i ^ + B y j ^ + B z k ^ then − B → = ( − B x ) i ^ + ( − B y ) j ^ + ( − B z ) k ^ Conclusion: In order show that A → ⋅ ( − B → ) = − A → ⋅ B → Substitute A x i ^ + A y j ^ + A z k ^ for A → , ( − A x ) i ^ + ( − A y ) j ^ + ( − A z ) k ^ for − A → , B x i ^ + B y j ^ + B z k

Physics for Science and Engineering With Modern Physics, VI - Student Study Guide

4th Edition

ISBN: 9780132273244

Author: Doug Giancoli

Publisher: PEARSON

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Chapter 7, Problem 19P

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Show that A→⋅(−B→)=−A→⋅B→.

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Chapter 7, Problem 18P

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Chapter 7 Solutions

Physics for Science and Engineering With Modern Physics, VI - Student Study Guide

Ch. 7.1 - A box is dragged a distance d across a floor by a...Ch. 7.1 - Return to the Chapter-Opening Question, page 163,...Ch. 7.4 - (a) Make a guess: will the work needed to...Ch. 7.4 - Can kinetic energy ever be negative?Ch. 7.4 - Prob. 1EE Ch. 7 - In what ways is the word work as used in everyday...Ch. 7 - A woman swimming upstream is not moving with...Ch. 7 - Can a centripetal force ever do work on an object?...Ch. 7 - Why is it tiring to push hard against a solid wall...Ch. 7 - Does the scalar product of two vectors depend on...

Ch. 7 - Can a dot product ever he negative? If yes, under...Ch. 7 - Prob. 7Q Ch. 7 - Does the dot product of two vectors have direction...Ch. 7 - Can the normal force on an object ever do work?...Ch. 7 - You have two springs that are identical except...Ch. 7 - Prob. 11Q Ch. 7 - In Example 710, it was stated that the block...Ch. 7 - Two bullets are fired at the same time with the...Ch. 7 - Does the net work done on a particle depend on the...Ch. 7 - A hand exerts a constant horizontal force on a...Ch. 7 - (I) How much work is done by the gravitational...Ch. 7 - (I) How high will a 1.85-kg rock go if thrown...Ch. 7 - (I) A 75.0-kg firefighter climbs a flight of...Ch. 7 - (I) A hammerhead with a mass of 2.0 kg is allowed...Ch. 7 - (II) Estimate the work you do to mow a lawn 10 m...Ch. 7 - (II) A lever such as that shown in Fig. 720 can be...Ch. 7 - (II) What is the minimum work needed to push a...Ch. 7 - (II) Eight books, each 4.0cm thick with mass 1.8...Ch. 7 - (II) A box of mass 6.0 kg is accelerated from rest...Ch. 7 - (II) (a) What magnitude force is required to give...Ch. 7 - (II) A 380-kg piano slides 3.9m down a 27 incline...Ch. 7 - (II) A gondola can carry 20 skiers, with a total...Ch. 7 - (II) A 17,000-kg jet takes off from an aircraft...Ch. 7 - (II) A 2200-N crate rests on the floor. How much...Ch. 7 - (II) A grocery cart with mass of 16 kg is being...Ch. 7 - (I) What is the dot product of...Ch. 7 - (I) For any vector V=Vxi+Vyj+Vzk show that...Ch. 7 - (I) Calculate the angle between the vectors:...Ch. 7 - Prob. 19P Ch. 7 - (I) Vector V1 points along the z axis and has...Ch. 7 - (II) Given the vector A=3.0i+1.5j, find a vector...Ch. 7 - (II) A constant force F=(2.0i+4.0j)N acts on an...Ch. 7 - (II) If A=9.0i8.5j,B=8.0i+7.1j+4.2k,and...Ch. 7 - (II) Prove that AB=AxBx+AyBy+AzBz, starting from...Ch. 7 - (II) Given vectors A=4.8i+6.8jandB=9.6i+6.7j,...Ch. 7 - (II) Show that if two nonparallel vectors have the...Ch. 7 - (II) Let V=20.0i+22.0j14.0k. What angles does this...Ch. 7 - (II) Use the scalar product to prove the law of...Ch. 7 - (II) Vectors A and B are in the xy plane and their...Ch. 7 - (II) A and B are two vectors in the xy plane that...Ch. 7 - (II) Suppose A=1.0i+1.0j2.0k and B=1.0i+1.0j+2.0k,...Ch. 7 - (II) Find a vector of unit length in the xy plane...Ch. 7 - (III) Show that the scalar product of two vectors...Ch. 7 - (I) In pedaling a bicycle uphill, a cyclist exerts...Ch. 7 - (II) A spring has k = 65N/m. 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Knowledge Booster

Show that A → ⋅ ( − B → ) = − A → ⋅ B → .

Solution Summary: The author illustrates how the dot product of two vectors stackrelto (A) and left (B) is shown.

Show that A→⋅(−B→)=−A→⋅B→.

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Chapter 7 Solutions