Question

How can I calculate the magnitude of vectors?

Answer 1

Hint: To get the solution for this question, use the distance formula which helps to find the distance between two points. First understand what vector means and then using an example find the magnitude of a vector that is mentioned in the example. The magnitude of a vector is normally represented using the modulus operator.
Formula used:
$\left| \overrightarrow{AB} \right|=\sqrt{{{({{x}_{1}}-{{x}_{0}})}^{2}}+{{({{y}_{1}}-{{y}_{0}})}^{2}}}$

Complete answer:
Vector is an object which has both the magnitude as well as direction. To find the magnitude of a vector, we need to calculate the length of the vector. Quantities such as velocity, displacement, force, momentum, etc. are vector quantities. But speed, mass, distance, volume, temperature, etc. are scalar quantities. Scalar quantity has only magnitude, whereas vectors have both magnitude and direction.
The magnitude of a vector formula is used to calculate the length for a given vector (say v) and is denoted as |v|. So basically, this quantity is the length between the initial point and endpoint of the vector. To calculate the magnitude of the vector, we can use the distance formula, which is shown below:
Suppose, AB is a vector quantity that has magnitude and direction both. To calculate the magnitude of the vector $\overrightarrow{AB}$, we must calculate the distance between the initial point A and endpoint B. In XY – plane, let A has coordinates $({{x}_{0}},{{y}_{0}})$ and B has coordinates $({{x}_{1}},{{y}_{1}})$. Therefore, by distance formula, the magnitude of vector $\overrightarrow{AB}$, can be written as:
$\left| \overrightarrow{AB} \right|=\sqrt{{{({{x}_{1}}-{{x}_{0}})}^{2}}+{{({{y}_{1}}-{{y}_{0}})}^{2}}}$

Note:
Vector is an important concept in physics, as many terms in physics have both magnitude and direction. Vector helps to identify the direction on which the term is applied, and the value of the vector tells the amount of term applied. Vectors help to find the resultant direction of force in many cases, where multiple forces are applied.