Magnitude of a Vector

Magnitude has different meaning in different areas like an earthquake having large magnitude means it was very powerful and devastating, or the amount of energy released is very high, in mathematics, magnitude relates numbers by power of 10. Sometimes it defines relative size etc.   

The Physical quantities can be divided into two sub-categories and they scalars and vectors. Only numerical numbers and proper units can be used to describe quantities such as mass or density. These amounts are known as “scalars.” However, quantities such as velocity or force need the declaration of a numerical value as well as a direction. Specifying the value of velocity, for example, is insufficient to define the motion of any object.                                                                                             

Vector: 

Vector is defined as a physical quantity which has defined magnitude and specified with a direction. It also must follow laws of vector addition. The vectors are 2-D Physical Quantity with magnitude as well-defined direction. A vector is represented as a line with an arrow pointing in the direction of the vector, and its length denotes the magnitude of the vector. The magnitude of the vector is the length of the line connecting two points A and B, and the direction of the displacement from point A to point B is the direction of the vector AB. Vectors have several uses in mathematics, physics, engineering, and a variety of other subjects.

Magnitude of vector 

The length of vector from its initial position or point to the final position is refer to its magnitude, It is also called as the modulus and it gives the absolute value of the vector. The magnitude is represented by mod A, |A|. 

The magnitude of a vector formula aids in the summarization of a vector’s numerical value. A vector has a magnitude and a well defined direction. This magnitude of a vector formula includes the independent values of the vector along the x-axis, y-axis, and z-axis. |v| stands for it. A vector’s magnitude must always be a positive integer or zero, and it cannot be negative. The length of a vector A is its magnitude, which is represented by |A|. Square root of sum of squares of the given vector’s components. The magnitude of a vector having direction ratios along the x, y, and z axes is equal to the square root of the sum of the squares of the vector’s direction ratios.

Magnitude formula

The length or size of a vector is referred to as Vector magnitude. It also determines its course. The Pythagorean theorem and the distance formula, which are used to generate the vector magnitude formula, are concepts underpinning these formulas. The magnitude of a vector having direction ratios along the x, y, and z axes is equal to the square root of the sum of the squares of its direction ratios.

There are few step to find the magnitude of any given vector with Magnitude formula.

• Step 1: Establish its components.

• Step 2: Add the squares of each of its components.

• Step 3: Now, the square root of the sum is obtained.

• For 2 D Vector: Let say P = P1 + P2 , then magnitude of P vector is √[ (P1 )2 + (P2 ) 2 ]

• For 3 D Vector: Let say P = P1 + P2 + P3, then magnitude of P vector is √[ (P1 )2 + (P2 ) 2 + (P3 )2]

Conclusion:

A vector formula’s magnitude helps in defining the numerical value of a given vector. The vector has a magnitude and a specific defined direction. This magnitude of a vector formula helps to determine the distinct vector measurements along the x-axis, y-axis, and z-axis. It is represented by the symbol |v|. A vector’s magnitude is either a positive integer or zero, and it can never be negative.