How to Find the Magnitude of a Vector

Step-by-Step Guide

1. 1

   Step 1: Determine the components of the vector.

   Every vector can be numerically represented in the Cartesian coordinate system with a horizontal (x-axis) and vertical (y-axis) component.It is written as an ordered pair v=<x,y>{\displaystyle v=<x,y>}.
   
   For example, the vector above has a horizontal component of 3 and a vertical component of
   -5, therefore the ordered pair is <3,
   -5>.
2. 2

   Step 2: Draw a vector triangle.

   When you draw the horizontal and vertical components, you end up with a right triangle.
   
   The magnitude of the vector is equal to the hypotenuse of the triangle so you can use the Pythagorean theorem to calculate it. , The Pythagorean theorem is A2 + B2 = C2. “A” and “B” are the horizontal and vertical components of the triangle while “C” is the hypotenuse.
   
   Since the vector is the hypotenuse you want to solve for “C”. x2 + y2 = v2 v = √(x2 + y2)) , Using the equation above, you can plug in the numbers of the ordered pair of the vector to solve for the magnitude.
   
   For example, v = √((32+(-5)2)) v =√(9 + 25) = √34 =
   5.831 Don't worry if your answer is not a whole number.
   
   Vector magnitudes can be decimals.
3. 3

   Step 3: Rearrange the Pythagorean theorem to calculate the magnitude.

4. 4

   Step 4: Solve for the magnitude.

Detailed Guide

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