How to Find Vector Size: 7 Steps (with Pictures)

2023 Author: Jason Gerald | [email protected]. Last modified: 2023-08-02 00:13

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

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 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, find "C".

• x² + y² = v²
• v = (x² + y²))

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 = ((3²+(-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

. 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 = ((x₂-x₁)² +(y₂-y₁)²) before finding the magnitude of the vector.

• Point A is the ordered pair 1 <x₁, y₁> and point B are consecutive pairs of 2 <x₂, y₂>

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 = ((x₂-x₁)² +(y₂-y₁)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.