Explanation Write the general expression for vector A → A → = A x i ^ + A y j ^ + A z k ^ (I) Here, A → is the vector, A x is the x component of the vector A → , A y is the y component of the vector A → , and A z is the z component of the vector A → . Find the desired quantity of dot product of a vector with itself gives the square of the magnitude of that vector. A → ⋅ A → = ( A x i ^ + A y j ^ + A z k ^ )

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN: 9781133939146

Author: Katz, Debora M.

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Instantaneous Power

Power is defined in physics as the amount of energy transmitted or transformed per unit time. The watt is the unit of electricity in the International System of Units, equivalent to one joule per second.

Question

Chapter 9, Problem 18PQ

To determine

Show that the dot product of vector gives square of vector A→⋅A→=A2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 17PQ

Chapter 9, Problem 19PQ

Students have asked these similar questions

Consider two vectors A = i +i+k and B = -i + j+ k. Which of the following statements about the given vectors is not true? O The dot product of the two vectors is equal to 1. O The cross product between the two vectors has a z-component equal to zero. O The magnitudes of the two vectors are the same. O The angle between the two vectors is 70.52°

E. Engagement Consider the vectors given below A = Azî + Ayĵ + A,k B = Bxî + Byj + B,k Get the dot product of A andB by following the steps below. A·B = (Azî + Ayĵ + A‚k)(Bxî + Byĵ + B,k) Step 1: Multiply the vectors, the way you multiply polynomials. You should get 9 terms. Ā ·B = Step 2: Rearrange your terms. Set side by side the components and the unit vector. A ·B = Step 3: Apply the dot products to your unit vectors. Recall: î · î = j· j = k · k = 1 and î ·j = î · k = j · k = 0 A·B =. Step 4: Write the simplified and the final dot product A·B =

Two vectors A and B are shown in the figure. The magnitude of their dot product is C, and the magnitude of their cross product is 1.094 C. Find cos(0). B A.

Chapter 9 Solutions

Physics for Scientists and Engineers: Foundations and Connections

Ch. 9.4 - In the three cases shown in Figure 9.11, a force...Ch. 9.6 - Prob. 9.2CE Ch. 9.6 - Prob. 9.3CE Ch. 9.7 - Prob. 9.4CE Ch. 9.7 - Prob. 9.5CE Ch. 9.9 - Prob. 9.6CE Ch. 9 - Pick an isolated system for the following...Ch. 9 - Prob. 2PQ Ch. 9 - Prob. 3PQ Ch. 9 - Prob. 4PQ

Ch. 9 - Prob. 5PQ Ch. 9 - Prob. 6PQ Ch. 9 - Prob. 7PQ Ch. 9 - A 537-kg trailer is hitched to a truck. Find the...Ch. 9 - Prob. 9PQ Ch. 9 - A helicopter rescues a trapped person of mass m =...Ch. 9 - Prob. 11PQ Ch. 9 - An object is subject to a force F=(512i134j) N...Ch. 9 - Prob. 13PQ Ch. 9 - Prob. 14PQ Ch. 9 - Prob. 15PQ Ch. 9 - Prob. 16PQ Ch. 9 - Prob. 17PQ Ch. 9 - Prob. 18PQ Ch. 9 - Prob. 19PQ Ch. 9 - Prob. 20PQ Ch. 9 - Prob. 21PQ Ch. 9 - Prob. 22PQ Ch. 9 - A constant force of magnitude 4.75 N is exerted on...Ch. 9 - In three cases, a force acts on a particle, and...Ch. 9 - An object of mass m = 5.8 kg moves under the...Ch. 9 - A nonconstant force is exerted on a particle as it...Ch. 9 - Prob. 27PQ Ch. 9 - Prob. 28PQ Ch. 9 - Prob. 29PQ Ch. 9 - A particle moves in the xy plane (Fig. P9.30) from...Ch. 9 - A small object is attached to two springs of the...Ch. 9 - Prob. 32PQ Ch. 9 - Prob. 33PQ Ch. 9 - Prob. 34PQ Ch. 9 - Prob. 35PQ Ch. 9 - Prob. 36PQ Ch. 9 - Prob. 37PQ Ch. 9 - Prob. 38PQ Ch. 9 - A shopper weighs 3.00 kg of apples on a...Ch. 9 - Prob. 40PQ Ch. 9 - Prob. 41PQ Ch. 9 - Prob. 42PQ Ch. 9 - Prob. 43PQ Ch. 9 - Prob. 44PQ Ch. 9 - Prob. 45PQ Ch. 9 - Prob. 46PQ Ch. 9 - Prob. 47PQ Ch. 9 - Prob. 48PQ Ch. 9 - Prob. 49PQ Ch. 9 - A small 0.65-kg box is launched from rest by a...Ch. 9 - A small 0.65-kg box is launched from rest by a...Ch. 9 - A horizontal spring with force constant k = 625...Ch. 9 - A box of mass m = 2.00 kg is dropped from rest...Ch. 9 - Prob. 54PQ Ch. 9 - Return to Example 9.9 and use the result to find...Ch. 9 - Prob. 56PQ Ch. 9 - Crall and Whipple design a loop-the-loop track for...Ch. 9 - Prob. 58PQ Ch. 9 - Calculate the force required to pull a stuffed toy...Ch. 9 - Prob. 60PQ Ch. 9 - Prob. 61PQ Ch. 9 - Prob. 62PQ Ch. 9 - An elevator motor moves a car with six people...Ch. 9 - Prob. 64PQ Ch. 9 - Figure P9.65A shows a crate attached to a rope...Ch. 9 - Prob. 66PQ Ch. 9 - Prob. 67PQ Ch. 9 - Prob. 68PQ Ch. 9 - Prob. 69PQ Ch. 9 - Prob. 70PQ Ch. 9 - Prob. 71PQ Ch. 9 - Estimate the power required for a boxer to jump...Ch. 9 - Prob. 73PQ Ch. 9 - Prob. 74PQ Ch. 9 - Prob. 75PQ Ch. 9 - Prob. 76PQ Ch. 9 - Prob. 77PQ Ch. 9 - Prob. 78PQ Ch. 9 - Prob. 79PQ Ch. 9 - A block of mass m = 0.250 kg is pressed against a...Ch. 9 - On a movie set, an alien spacecraft is to be...Ch. 9 - Prob. 82PQ Ch. 9 - A spring-loaded toy gun is aimed vertically and...Ch. 9 - Prob. 84PQ Ch. 9 - The motion of a box of mass m = 2.00 kg along the...Ch. 9 - Prob. 86PQ Ch. 9 - Prob. 87PQ Ch. 9 - Prob. 88PQ

Knowledge Booster

Learn more about

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

Show that the dot product of vector gives square of vector A → ⋅ A → = A 2 .

Solution Summary: The author demonstrates that the dot product of a vector with itself gives the square of the magnitude of that vector.

Concept explainers

Show that the dot product of vector gives square of vector A→⋅A→=A2.

Want to see the full answer?

Chapter 9 Solutions