# 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**= (v*, v*_{1}*) be a vector in space 2, then the norm of vector*_{2}**v**is expressed as,
And it is illustrated with Figure 1,

Suppose that

**v**= (v*, v*_{1}*, v*_{2}*) is a vector in space 3. Using Figure 2,*_{3}
Then we get it

so,

If P

*(x*_{1}*, y*_{1}*, z*_{1}*) and P*_{1}*(x*_{2}*, y*_{2}*, z*_{2}*) are two points in space 3, then the distance d between the two points is the length of the vector P*_{2}*P*_{1}*(Figure 3),*_{2}
because,

So based on the norm vector formula in Space 3, it is clear that

Likewise P

_{1}(x_{1}, y_{1}) and P_{2}(y_{1}, y_{2}) 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 P

_{1}(2, -1, -5) and point P_{2}(4, -3, 1) areSUBSCRIBE TO OUR NEWSLETTER

## 0 Response to "Calculating the Length of a Vector"

## Post a Comment