Undergrad Absolute value bars in dot product derivation

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The absolute value bars in the dot product derivation represent the length of the vector rather than the absolute value of a number. This notation is used because the length of a vector is always positive. The convention of using absolute value bars was more common in earlier vector mathematics texts, while modern texts often prefer double v-bar notation. Understanding this distinction is crucial for correctly interpreting vector operations. The discussion highlights the evolution of notation in vector mathematics.
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Dose someone please know why they have the absolute value bars in this derivation?

1679290283120.png

many thanks!
 
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The absolute value bars indicate the length of the vector not absolute value of a number.

Of course, the vector length is always positive.

I think this convention was more popular in early vector math books where as now they use the double v-bar notation.

https://en.wikipedia.org/wiki/Norm_(mathematics)
 
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jedishrfu said:
The absolute value bars indicate the length of the vector not absolute value of a number.

Of course, the vector length is always positive.

I think this convention was more popular in early vector math books where as now they use the double v-bar notation.

https://en.wikipedia.org/wiki/Norm_(mathematics)
Thank you for your help @jedishrfu !
 

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