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Finding the Vector Magnitude of a Line Segment

Vector magnitude is the distance between the initial point and terminal point of a directed line segment. Here is a picture of vector AB:

Vector magnitude: Picture of vector AB

The length of the vector, in this case, is expressed as absolute value AB (|AB|).

Vector Magnitude Formula

This is the formula for the magnitude of a vector. You can find the length of a vector by subtracting and squaring the x and y values, respectively. Then, you'll add these two values together and take the square root:

Formula for vector magnitude

See the below figure of vec SQRT:

Vector magnitude: Figure of vector SQRT

Because the coordinates are given, we can use them to find the magnitude of the vector SQ (rounded to the first decimal point).

Vector magnitude: Formula in finding the magnitude of the vector SQ

Vector magnitude: Formula in finding the magnitude of the vector SQ

Vector magnitude: Formula in finding the magnitude of the vector SQ

Vector magnitude: Formula in finding the magnitude of the vector SQ

Formula in finding the magnitude of the vector SQ

Component Form of a Vector

To find the component form of a vector, you must calculate the changes in x and y values from one set of coordinates to the other.

Let’s demonstrate using vector RT. Simply subtract the x and y values of each ordered pair:

Formula in finding the magnitude of vector RT

Formula in finding the magnitude of vector RT

Formula in finding the magnitude of vector RT

Vector Direction Formula

In trigonometry, confusing the terms vector and scalar is common. They both contain values that are measured in magnitudes. However, scalars are purely defined by their magnitude. For example, speed, volume, mass, and time are all scalar quantities.

Vectors are different from scalars because they also have a direction. The direction of the vector is its angle along the x-axis. Here’s what this angle looks like.

Graph showing the formula of vector direction

The following formula can be used to determine the angle:

Formula of vector direction

Finding vector magnitude helps you determine how much a line segment has traveled from one set of points to another. Furthermore, finding the angle of its direction allows you to fully measure the quantity of a vector. To learn more about vectors, review vector addition and subtraction.

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