Vector Magnitude

If an object (a) has magnitudes along with direction, it is known as a vector. To determine the magnitude, we require to measure the length of the vector. e.g., momentum, velocity, displacement, energy, etc.

A vector's magnitude is applied to determine the length for a given vector ( suppose: v ), then the magnitude of vector v is denoted as |v|. So fundamentally, this amount is the length between the initial point and the final point of the vector. To determine the magnitude of the vector, we apply the distance formula, which we will discuss below:

 

Formula of Vector Magnitude Calculator

Assume AB is a vector quantity possessing both magnitude and direction. To determine the vector AB's magnitude, we have to measure the distance in the initial point A and final point B. In XY – plane, let A holds coordinates (x0, y0) and B holds coordinates (x1, y1). Hence, by applying the distance formula, the magnitude of vector AB can be formulated as:

\[|\overrightarrow {AB} | = \sqrt {\mathop {\left( {\mathop x\nolimits_1 - \mathop x\nolimits_0 } \right)}\nolimits^2 + \mathop {\left( {\mathop y\nolimits_1 - \mathop y\nolimits_0 } \right)}\nolimits^2 } \]

Note:

To know about unit vectors, you can use our Unit Vector Calculator.

Example

For more clear understanding let’s have a look at the example below:

Determine the magnitude of the vector AB having (1, 2) coordinates in initial point A and (4, 3) coordinates in final point B.

Given data

A = (1, 2)
B = (4, 3)

To Find

The magnitude of the vector = ?

Solution

To get the magnitude of the vector, we will use the formula listed below:

\[|\overrightarrow {AB} | = \sqrt {\mathop {\left( {\mathop x\nolimits_1 - \mathop x\nolimits_0 } \right)}\nolimits^2 + \mathop {\left( {\mathop y\nolimits_1 - \mathop y\nolimits_0 } \right)}\nolimits^2 } \]

From the above formula, let’s get the value of

x0 = 1
y0 = 2
x1 = 4
y1 = 3

Using the distance formula,

\[|\overrightarrow {AB} | = \sqrt {\mathop {\left( {4 - 1} \right)}\nolimits^2 + \mathop {\left( {3 - 2} \right)}\nolimits^2 } \] \[|\overrightarrow {AB} | = \sqrt {\mathop {\left( 3 \right)}\nolimits^2 + \mathop {\left( 1 \right)}\nolimits^2 } \] \[|\overrightarrow {AB} | = \sqrt {9 + 1} = \sqrt {10} \]

The magnitude of |AB| is

\[|\overrightarrow {AB} | = 10\]

How to use Vector Magnitude Calculator?

The steps to use a vector magnitude calculator are as follows:

Step 1: Enter the value of vector A in the required input.

Step 2: Enter the value of vector B in the required input.

Step 3: The calculator will automatically display an answer on the screen.

Calculator use

What function does a magnitude of a Vector calculator perform? You have to add coordinates values, and in a few moments, the calculator will display results on the screen. It gets the prescribed solution to your problems. To resolve complex issues, you can use this calculator.