Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 12.1, Problem 12.17P
To determine
The check the validity of the equation:
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem 4: It should be obvious that the magnitude of a vector is independent of the
choice of coordinate system. This implies that r r is the same for any set of axes. Use this
to prove that the dot product of two different vectors r.s is also independent of coordinate
system. [Hint: Consider the length of r + s.]
Prove that the scalar product of a relative covariant vector of weight w and a relative contravariant
vector of weight w' is a relative scalar of weight w+ w'.
Two vectors in Cartisian coordinates have components A= (2,2,3) and B =(4,-1,7). What is the dot product of vector A with Vector B?
Chapter 12 Solutions
Introduction to Electrodynamics
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.Similar questions
- Problem 7: Two vectors in Cartesian coordinates have components A = (3, 2, 3) and B = (4, -1,7). What is the dot product of vector A with vector B? A B = | sin() cotan() atan() cosh() cos() asin() acotan() tanh() O Degrees tan() acos() sinh() cotanh() Radians П () 7 8 E ^^ 4 / 1 + * 5 2 0 BACKSPACE 963 HOME END DEL CLEARarrow_forwardGiven the points M(0.1, -0.2, -0.1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector RMN; (b)the dot product RMN. RMP ; (c) the scalar projection of RMN on RMP; (d) the vector projection of RMN on RMP; (e) the angle between RMN on RMP.arrow_forwardProblem no 1: Find sum, difference and scalar and vetor product of vectors u=[−4,6],w=[0,4]. Draw and calculate.arrow_forward
- The scalar triple product of three vectors is a • (b x c). Prove that the scalar triple product will not change when you cyclically permute the three vectors. (i.e., prove that a • (b x c) = b • (c x a) = c • (a x b) )arrow_forwardrection: Calculate the following. (Three points each) 2. Sam has measured the end points of two poles, and wants to know the angle between them: 1. Calculate the dot product of vectors a and b: (11,5,8) A (3.60 m) a (4,8,2) az k 70.0 30.0 () ax y B (2.40 m) ay 3. Vector a has magnitude 3, vector b has magnitude 4 and the angle between a and b is 60°. What is the value of a. b.? 4. Vector a has magnitude 3v2, vector b has magnitude 5 and the angle between a and b is 135°. What is the value of a. b.? 5. What is the size of the angle between the vectors a = (2, 5, -1) and b = (-3, 2, 6)?arrow_forwardUsing the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A-21-9) and B=31-5j 24.20 x Your response differs from the correct answer by more than 10%. Double check your calculations." (b) A=-61+ 7) and B=31-4) + 2k 168.35 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out al (c) A=1-21 +2k and B = 3] + 4k 60 X Your response differs from the correct answer by more than 10%. Double check your calculations.arrow_forward
- Given that vector u has length 3, vector v has length 5, and the dot product of u and v is -1, what is the length of 2u-v?arrow_forward(a) Find the scalar products î · î, ĵ· ĵ, and k · Ê. (b) Find î · ĵ, ĵ · k, and k · î (c) Use the distributive law to multiply out the scalar product of two arbitrary vectors à Axî + Ayî + A¸k and B Equation 6.4. Bxî + Byĵ + Bzk, and use the results of (a) and (b) to verifyarrow_forwardUsing Gram-Schmidt algorithm, check for linear independence of the following vectors: v= (1, -2, 1, -1), v2= (1, 1, 3, -1), and v3= (-3, 7, 1, 3).arrow_forward
- Find the direction cosines of the vectors whose direction Ratios are (3, 4, 5) and ( 1, 2, -3). Hence find the angle between the two vectorsarrow_forwardThe angle between two vectors is u. (a) If u = 30.0o, which has the greater magnitude: the scalar product or the vector product of the two vectors? (b) For what value (or values) of u are the magnitudes of the scalar product and the vector product equal?arrow_forwardProve the property of the cross product u × v = 0 if and only if u and v are scalar multiples of each other.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY