Question

How do we represent the magnitude of a vector in physics?

Answer 1

In order to answer the given question, we need to know the concept of vectors and its representation. Also, we need to know about the magnitude of any quantity. After that only, we can finally conclude with the correct answer of the given question.

Complete step by step answer:
Step one
First of all let us define the magnitude. The magnitude of a quantity is the numerical value of that quantity. For example: If we write the value of force to be $5N$, so here $5$ is the magnitude and $N$ is the unit of force.
Step two
Now let us find out about the magnitude of the vector quantity. We know that the magnitude of a vector gives its length. In other words we can say that by writing the magnitude of a vector, we actually calculate its length.
Step three
Now let us write down the expression for the magnitude of a vector.

Let us consider a vector $\overrightarrow {AB}$. The positions of the vector are mentioned on their respective axis.
We know that the magnitude of the vector will give us the length of the vector.
Therefore, $\left| {\overrightarrow {AB} } \right| = \sqrt {{{({x_1} - {x_0})}^2} + {{({y_1} - {y_0})}^2}}$
$\Rightarrow \left| {\overrightarrow {AB} } \right| = \sqrt {{x^2} + {y^2}}$
Hence, the magnitude of a vector can be represented as $\left| {\overrightarrow {AB} } \right| = \sqrt {{x^2} + {y^2}}$.

Note:
A vector is a quantity which has both magnitude and a direction. A vector quantity is represented by a line with an arrow head. The starting point of the line is known as tail and the arrow head is known as the head of the vector. We measure the vector quantity from the tail to head.