Vector Magnitude Calculator

What is a vector?

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.

Vector Magnitude Calculator Explanation

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

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;

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

Examples

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.

Solution

Given data

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

To find

The magnitude of the vector = ?

we know,

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

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

x0 = 1
y0 = 2
x1 = 4
y1 = 3

Using 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

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

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.