A vector is a geometric object that has both magnitude and direction. The magnitude of the vector is the length, while the direction of the resultant vector is the direction. The size of a vector can be found in a few easy steps. Some other important vector operations include adding and subtracting vectors, finding angles between two vectors, and finding cross products.

## Step

### Method 1 of 2: Finding the Vector Size from the Origin

#### Step 1. Determine the components of the vector

Each vector can be represented numerically in a Cartesian coordinate system with horizontal (x-axis) and vertical (y-axis) components. These components are written in consecutive pairs $v=,\; y="">\{displaystyle\; v=\}$

### Misalnya, vektor di atas memiliki komponen horizontal 3 dan komponen vertikal -5, dengan demikian pasangan berurutannya adalah

#### Step 2. Vector image of a triangle

When describing the horizontal and vertical components, we get a right triangle. The magnitude of a vector is equal to the length of the hypotenuse of the triangle so we can use the Pythagorean Theorem to calculate it.

#### Step 3. Change the Pythagorean Theorem formula to calculate the magnitude of the vector

The formula for the Pythagorean theorem is A^{2} + B^{2} = C^{2}. “A” and “B” are the horizontal and vertical components of the triangle while “C” is the hypotenuse. Since the vector is the hypotenuse, find "C".

- x
^{2}+ y^{2}= v^{2} - v = (x
^{2}+ y^{2}))

#### Step 4. Find the magnitude of the vector

Using the equation above, enter the numbers in consecutive pairs of vectors to find the magnitude of the vector.

- For example, v = ((3
^{2}+(-5)^{2})) - v =√(9 + 25) = 34 = 5, 831
- Don't worry if your answer is not an integer. The vector size can be in decimal form.

### Method 2 of 2: Finding the Size of a Vector Not from the Origin

#### Step 1. Determine the components of the two points on the vector

Each vector can be represented numerically in a Cartesian coordinate system with horizontal (x-axis) and vertical (y-axis) components. These components are written in consecutive pairs $v=,\; y="">\{displaystyle\; v=\}$

. Jika Anda diberi vektor yang tidak berawal dari titik asal pada koordinat Kartesian, Anda harus mendefinisikan komponen kedua titik pada vektor.

- Misalnya, vektor AB memiliki pasangan berurutan pada titik A dan titik B.
- Titik A memiliki komponen horizontal 5 dan komponen vertikal 1, sehingga pasangan berurutannya adalah.
- Titik B memiliki komponen horizontal 1 dan komponen vertikal 2, sehingga pasangan berurutannya adalah.

#### Step 2. Use the modified formula to find the magnitude of the vector

Now that you know the two points needed, subtract the x and y components from each using the formula v = ((x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}) before finding the magnitude of the vector.

- Point A is the ordered pair 1 <x
_{1}, y_{1}> and point B are consecutive pairs of 2 <x_{2}, y_{2}>

#### Step 3. Find the magnitude of the vector

Enter the number of consecutive pairs and calculate the magnitude of the vector. Using the example above, the calculation is as follows:

- 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
- Don't worry if your answer is not an integer. The vector size can be in decimal form.