Content

• Steps

Vector is a geometric element with magnitude and direction. The magnitude of a vector is its length, and the direction of the vector indicates its direction. To calculate the magnitude of the vector, it only takes a few simple math operations. In addition, we can add or subtract two vectors, find the angle between the two vectors as well as calculate the directional product of the two vectors.

Steps

Method 1 of 2: Find the magnitude of a vector originated at point O

1. 

   Determine the composition of the vector. Each vector can be represented on the oxygen coordinate system (Carteian coordinate system) in the horizontal (x) and vertical (y) axis. When writing vector coordinates, x and y coordinates are written in order.
   • For example, the vector in the figure has the coordinate point on the horizontal axis 3 and the coordinate on the vertical axis is -5, so we write the coordinates of this vector as <3, -5>.

2. 

   
   
   Draw a vector triangle. From the end of the vector, lower the perpendicular to the vertical and horizontal axis, and we will get two equal right triangles. The magnitude of the vector being considered is the hypotenuse length of this triangle, so we just need to apply the Pythagorean theorem to calculate its value.

3. 

   
   
   Rearrange the Pythagorean theorem to calculate the length. Pythagorean Theorem: A + B = C. Where "A" and "B" are the horizontal and vertical coordinates of the triangle, "C" is the hypotenuse of the triangle. Since the vector being considered is also the hypotenuse "C", we need to find "C".
   • x + y = v
   • v = √ (x + y))

4. 

   
   
   Solve equations to find the vector magnitude. Substitute the values ​​into the respective quantities and solve the equation to get the magnitude of the vector in question.
   • For example, v = √ ((3 + (- 5)))
   • v = √ (9 + 25) = √34 = 5,831
   • Vector can be a decimal, so don't worry if the calculated result is not an integer.
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Method 2 of 2: Calculate the vector magnitude outside the origin

1. 

   Determine the beginning and end of the vector. All vectors can be represented on a Cartesian coordinate system in terms of coordinates with respect to the horizontal (x axis) and vertical (y) axis. The coordinates of each point will be written in pairs of x and y as follows:. If the problem says that the vector is not on the coordinate axis in the Cartesian coordinate system, we need to determine the coordinates of the beginning and the end of the vector.
   • For example, the vector AB is written in pairs and in the order of point A and then point B.
   • The point A has the horizontal coordinate of 5 and the vertical coordinate is 1, so the point A coordinate is <5.1>.
   • The point B has the horizontal coordinate of 1 and the vertical coordinate is 2, so the point B coordinate is <1,2>.

2. 

   Use the modified formula to calculate the magnitude of the vector. Now that we have the coordinates of the beginning and end points of the vector, we need to take the coordinates of the coordinates x and y of these two points, then apply the formula v = √ ((x₂-x₁) + (y₂-y₁)).
   • Inside <>₁, y₁> is the coordinate of point A, point B has a pair of coordinates <>₂, y₂>.

3. 

   Solve the equation. Assign corresponding x, y values ​​into the formula and solve the equation to get the magnitude of the vector. Using the example above, we can calculate the following:
   • v = √ ((x₂-x₁) + (y₂-y₁))
   • v = √ ((1-5) + (2-1))
   • v = √ ((- 4) + (1))
   • 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.
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