About The magnitude of Vector formula
A vector is a quantity that has both magnitudes as well as direction. Some physical quantities such as displacement, velocity and acceleration belong to this category. But not all Physical quantities involve a direction. Temperature, speed and distance are defined by their magnitude only.
Any vector is denoted by an arrow. The length of the arrow shows its magnitude and the arrowhead points in the direction.Now if we want to find the length of any given vector, we can use Vector Formula. Let's see how.
The magnitude of a Vector Formula
The magnitude of a given vector is calculated by the vector formula. This quantity is used to define the length between the initial point and the end point of any given vector.
If one of its endpoints is at origin (0,0) and the other end point is at (x, y), its magnitude is: |v| =√(x2 + y2)
Also ,For a vector B = x1 i + y1 j + z1 k, its magnitude is: |B| =√(x12 + y12 + z12)
Note: The magnitude of a vector can never be negative as squaring converts all negative values to positive ones.
Let us understand the application of magnitude of a vector formula using the below solved examples:
Solved example of Magnitude of Vector formula
Example 1:Using the magnitude formula, find the magnitude of the vector with A = (4, 3)?
Solution: |A| = √(x2+ y2)
=√(42 + 32)
= √25=5 units
>Example 2: Using the Magnitude formula, find the magnitude of the vector A= i + 4j - 5k.
Solution:|A| =√(12 + (4)2 + (-5)2)
= √(1+16+25) =√42 units
Example 3: Find the magnitude of a vector joining (1,5) and (3,4).
Solution: Magnitude= |A| =√(3-1)2 + (4-5)2√4+1 =√5 units
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