Absolute value bars in dot product derivation

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The discussion clarifies that absolute value bars in vector mathematics denote the length of a vector, not the absolute value of a number. This convention indicates that vector lengths are inherently positive. The use of absolute value bars has become less common, with the double v-bar notation gaining popularity in contemporary texts. For further reference, the Wikipedia page on vector norms provides additional context.

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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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