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A vector is a geometric element with magnitude and direction. [1] X Research Source The magnitude of a vector is its length, and the direction of the vector indicates its direction. To calculate the magnitude of a vector we just need to do some simple math. In addition, we can also perform addition or subtraction of two vectors, find the angle between two vectors as well as calculate the directed product of two vectors.
Steps
Find the magnitude of a vector with origin at point O
- For example, the vector in the figure has point coordinates on the horizontal axis of 3 and coordinates on the vertical axis of -5, so we write the coordinates of this vector as <3, -5>.
- x 2 + y 2 = v 2
- v = (x 2 + y 2 ))
- For example, v = ((3 2 +(-5) 2 ))
- v =√(9 + 25) = 34 = 5,831
- The vector can be a decimal, so don’t worry if the calculated result is not an integer.
Calculate the magnitude of the vector outside the origin
- For example, the vector AB is written in pairs and in the order of point A then point B.
- Point A has horizontal coordinates of 5 and vertical coordinates of 1, so point A coordinates are <5,1>.
- Point B has horizontal coordinates of 1 and vertical coordinates of 2, so the coordinates of point B are <1,2>.
- Where <x 1 , y 1 > are the coordinates of point A, point B has a coordinate pair <x 2 , y 2 >.
- v = ((x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 )
- v = ((1-5) 2 +(2-1) 2 )
- v = ((-4) 2 +(1) 2 )
- v = (16+1) = (17) = 4.12
- Since the magnitude of the vector can be a decimal, don’t worry if the calculated result is not an integer.
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 12 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 178,350 times.
A vector is a geometric element with magnitude and direction. [1] X Research Source The magnitude of a vector is its length, and the direction of the vector indicates its direction. To calculate the magnitude of a vector we just need to do some simple math. In addition, we can also perform addition or subtraction of two vectors, find the angle between two vectors as well as calculate the directed product of two vectors.
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