Calculating the Length of a Vector
The length of a vector v is often called the v norm and is expressed as |v|. Let v = (v1, v2) be a vector in space 2, then the norm of
vector v is expressed as,
And it is illustrated with Figure 1,
Suppose that v = (v1, v2,
v3) is a vector in space
3. Using Figure 2,
Then we get it
so,
If P1(x1,
y1, z1) and P2(x2, y2, z2)
are two points in space 3, then the distance d between the two points is the
length of the vector P1P2 (Figure 3),
because,
So based on the norm vector formula in Space 3, it is clear that
Likewise P1 (x1,
y1) and P2 (y1, y2) are two points
in space 2, then the distance between the two points is determined by:
Example 1.
The length of the vector v = (-3, 2, 1) is
The distance d between
points P1 (2, -1, -5) and point P2 (4, -3, 1) are
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