Definition
Magnitude
Magnitude tells how large a quantity is; for a vector, it is the vector’s non-negative length.
What it means
A vector tells both how far and which way. Its magnitude keeps the “how far” part and leaves out the direction. Zero is allowed, so magnitude is non-negative, not always positive.
Remember it
Magnitude answers “how much?”—not “which way?”
Example
For v = ⟨3, 4⟩, the magnitude is √(3² + 4²) = √25 = 5.
Watch for
Vectors pointing in opposite directions can have the same magnitude because direction is not part of the magnitude.
Common mix-up
A component such as −3 can be negative, but a vector’s magnitude cannot be negative.
Exact meaning
Magnitude is the non-negative size of a mathematical quantity; for a vector, it is the vector’s length and does not include direction.