Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(III) Let $\vec{\mathbf{A}}, \vec{\mathbf{B}},$ and $\vec{\mathbf{C}}$ be three vectors, which for generality we assume do not all lie in the same plane. Show that$$\vec{\mathbf{A}} \cdot(\vec{\mathbf{B}} \times \vec{\mathbf{C}})=\vec{\mathbf{B}} \cdot(\vec{\mathbf{C}} \times \vec{\mathbf{A}})=\vec{\mathbf{C}} \cdot(\vec{\mathbf{A}} \times \vec{\mathbf{B}})$$

Get the answer to your homework problem.

Try Numerade free for 7 days

Input your name and email to request the answer

Like

Report

$$\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}=\hat{\mathbf{i}}\left(A_{y} B_{z}-A_{z} B_{y}\right)+\hat{\mathbf{j}}\left(A_{z} B_{x}-A_{x} B_{z}\right)+\hat{\mathbf{k}}\left(A_{x} B_{y}-A_{y} B_{x}\right)$$$$\overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{C}}=\hat{\mathbf{i}}\left(B_{y} C_{z}-B_{z} C_{y}\right)+\hat{\mathbf{j}}\left(B_{z} C_{x}-B_{x} C_{z}\right)+\hat{\mathbf{k}}\left(B_{x} C_{y}-B_{y} C_{x}\right)$$$$\overrightarrow{\mathbf{C}} \times \overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}\left(C_{y} A_{z}-C_{z} A_{y}\right)+\hat{\mathbf{j}}\left(C_{z} A_{x}-C_{x} A_{z}\right)+\hat{\mathbf{k}}\left(C_{x} A_{y}-C_{y} A_{x}\right)$$

Physics 101 Mechanics

Chapter 11

Angular Momentum; General Rotation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

McMaster University

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

02:19

Given the three nonzero veβ¦

02:15

Let $\mathbf{u}, \mathbf{vβ¦

01:38

Prove that if $\mathbf{u},β¦

03:24

Another operation with vecβ¦

03:19

No transcript available

View More Answers From This Book

Find Another Textbook

05:36

An automobile traveling 50.0 km/h has tires of 65.0 cm diameter. (a) What isβ¦

04:56

In the instant of the figure, two particles move in an xy plane. Particle Ptβ¦

02:57

17_ A soft foam block of friction in mass m slides without At time the positβ¦

01:35

014 (part 1 of 8) 10.0 points Consider the plot below describing motion alβ¦

01:34

par CWhat is the rms speed of an oxygen gas molecule at room temperatureβ¦

03:05

What is the sound power level Lw of an acoustic source that produces: a 40 Wβ¦

08:06

A work station is to be located 3 m from a conveyor belt generating a sound β¦

04:16

12-17 A particle is moving with a velocity of Vo when $ = 0 and 0. If it is β¦

02:01

An electron of mass me 9.11 X 10 31 kg and charge of qe = .60 10 - 19 C is rβ¦

If F =7.2kN determine the magnitude of the resultant force acting on the scrβ¦