The magnitude of a vector quantity is usually represented by the same letter used for the vector, but in italic with no arrow on top. An alternative notation is the vector symbol with vertical bars on both sides. The two notations are shown below:
(Magnitude of V) = V = |V|
By definition the magnitude of a vector quantity is a scalar quantity (a number) and is always positive.
If r = (x, y, z)
represents the vector displacement of point R from the origin, what is the distance between these two points? In other words, what is the length, or magnitude,
r = |r|,
of vector r. It follows from a 3-dimensional generalization of Pythagoras' theorem that
r = (x2+y2+z2)1/2
Note that if
r = r1 + r2
|r| ≤ | r1|+ |r2|
In other words, the magnitudes of vectors cannot, be added algebraically. The only exception to this rule represented by the equality sign in the above expression) occurs when all the vectors in question point in the same direction.
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