Can the magnitude of vector be negative?

In summary, scalars can be negative, but the magnitude of a vector is always positive. The terms "absolute value" and "magnitude" are used interchangeably when referring to a vector's length. However, the absolute value is typically used when talking about a number while magnitude is used when talking about a vector. The magnitude of a vector is also known as its norm or length and is always positive. However, there are scalars that can be negative, such as the scalar product of two vectors.
  • #1
Red_CCF
532
0
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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  • #2
no, the magnitude of a vector is computed by sqrt(x1^2 + ... xn^2)
 
  • #3
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.
 
  • #4
the absolute value of a vector is the "norm"
 
  • #5
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).
 

1. Can a vector have a negative magnitude?

No, the magnitude of a vector is always a positive value. It represents the length or size of the vector and therefore cannot be negative.

2. What does a negative magnitude indicate?

A negative magnitude does not have a physical meaning in the context of vectors. It could be a result of an error in calculation or a misuse of vector notation.

3. Can a negative vector have a negative magnitude?

No, a vector with negative components can still have a positive magnitude. The magnitude is calculated by taking the square root of the sum of the squared components, so it will always be positive.

4. Can the magnitude of a vector be zero?

Yes, the magnitude of a vector can be zero if all of its components are zero. This represents a vector with no direction or magnitude, also known as a zero vector.

5. Why is the magnitude of a vector always positive?

The magnitude of a vector is always positive because it represents a physical quantity, such as distance or force, which cannot be negative. The magnitude is a measure of the size of the vector, not its direction.

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