Can the magnitude of vector be negative?

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SUMMARY

The magnitude of a vector is always a non-negative scalar, computed using the formula sqrt(x1^2 + ... + xn^2). While scalars can be negative, they do not represent the magnitude of a vector. The terms "absolute value" and "magnitude" are distinct; "absolute value" refers to numbers, while "magnitude" pertains to vectors. The magnitude, also known as the norm or length, of a vector is always positive or zero, distinguishing it from scalars that can be negative, such as those resulting from the scalar product (dot product) of two vectors.

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Red_CCF
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Recently I was told that scalars, although magnitude only, can be negative. Does this mean that the magnitude of a vector can be negative too?

Also, I'm wondering if there's a difference between the absolute value and magnitude of a vector like -3i-4j. Thanks for any help that you can provide
 
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no, the magnitude of a vector is computed by sqrt(x1^2 + ... xn^2)
 
Red_CCF said:
Also, I'm wondering if there's a difference between the absolute value and magnitude of a vector like -3i-4j. Thanks for any help that you can provide

I say "absolute value" only when I'm talking about a number, and "magnitude" when I'm talking about a vector. I don't know if it's actually incorrect to say "absolute value of a vector." Nevertheless, I don't think there's any chance you would confuse people by saying "absolute value of a vector," because I can't think of anything else besides the magnitude that it could be interpreted to mean.
 
the absolute value of a vector is the "norm"
 
The magnitude (a.k.a. norm or length) ǁaǁ of a vector a is a scalar and is always positive (or zero).

But there are scalars that are not magnitudes of vectors and they can be negative. (For example the scalar product (a.k.a. dot product or inner product) of two vectors a.b).
 

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