Does the book have an error in the addition of these two vectors?

In summary, the conversation discusses finding a unit vector in the direction of ##-\vec M - 2\vec N##, which is calculated to be ##0.923\hat a_x+0.355\hat a_y+0.142\hat a_z##. However, the book gives a slightly different answer of ##0.92\hat a_x+0.36\hat a_y+0.4\hat a_z##, which may be a typo.
  • #1
CaliforniaRoll88
35
6
Homework Statement
Given the vectors ##\vec M = -10\hat a_x+4\hat a_y-8\hat a_z## and ##\vec N = 8\hat a_x+7\hat a_y-2\hat a_z## , find: (a) a unit vector in the direction of ##-\vec M - 2\vec N##
Relevant Equations
##\hat a_B=\frac {\vec B} {\sqrt {B^2_x+B^2_y +B^2_z}}##
(a)
$$\vec A = -\vec M+2\vec N=26\hat a_x+10\hat a_y+4\hat a_z$$
Unit Vector Formula
$$\hat a_A=\frac{26\hat a_x+10\hat a_y+4\hat a_z}{\sqrt {26^2+10^2+4^2}}$$
$$0.923\hat a_x+0.355\hat a_y+0.142\hat a_z$$
The book gives ##0.92\hat a_x+0.36\hat a_y+0.4\hat a_z##
Not sure how the book get 0.4 for the z-component. Maybe it's an error.
 
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  • #2
CaliforniaRoll88 said:
Homework Statement: Given the vectors ##\vec M = -10\hat a_x+4\hat a_y-8\hat a_z## and ##\vec N = 8\hat a_x+7\hat a_y-2\hat a_z## , find: (a) a unit vector in the direction of ##-\vec M - 2\vec N##
CaliforniaRoll88 said:
$$\vec A = -\vec M+2\vec N=26\hat a_x+10\hat a_y+4\hat a_z$$
I assume that the latter is correct (plus sign, not minus, in front of ##2N##).
CaliforniaRoll88 said:
$$0.923\hat a_x+0.355\hat a_y+0.142\hat a_z$$
The book gives ##0.92\hat a_x+0.36\hat a_y+0.4\hat a_z##
Not sure how the book get 0.4 for the z-component. Maybe it's an error.
Considering that the answer is given with two significant figures and that ##0.4## only has one, this looks like a typo (missing 1).
 
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Likes CaliforniaRoll88 and PeroK
  • #3
Much appreciated.
 

1. What is the purpose of adding two vectors in a book?

The purpose of adding two vectors in a book is to demonstrate mathematical concepts and principles, such as vector addition, in a visual and practical way.

2. How do you know if there is an error in the addition of two vectors in a book?

You can check for errors in the addition of two vectors by following the steps outlined in the book and comparing your results to the correct answer. If your answer does not match the correct answer, there may be an error in the addition of the vectors.

3. Can errors in the addition of two vectors in a book affect the overall understanding of the topic?

Yes, errors in the addition of two vectors can affect the overall understanding of the topic. If the addition is incorrect, it can lead to incorrect conclusions and misunderstandings about the concept being taught.

4. What should I do if I find an error in the addition of two vectors in a book?

If you find an error in the addition of two vectors in a book, you should first double-check your own calculations to ensure that you have not made a mistake. If the error persists, you can reach out to the author or publisher of the book to report the error.

5. Are errors in the addition of two vectors common in books?

While errors in the addition of two vectors can occur in books, they are not very common. Most books go through multiple rounds of editing and review to ensure accuracy. However, it is always important to double-check your work and bring any errors to the attention of the author or publisher.

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