How can the sum of two vectors be found
The sum of two vectors can be found by adding their corresponding components.
If we have two vectors in a 2D space, vector A = (Ax, Ay) and vector B = (Bx, By), then their sum vector C = A + B can be found by adding their respective components:
Cx = Ax + Bx
Cy = Ay + By
Similarly, if we have two vectors in a 3D space, vector A = (Ax, Ay, Az) and vector B = (Bx, By, Bz), then their sum vector C = A + B can be found by adding their respective components:
Cx = Ax + Bx
Cy = Ay + By
Cz = Az + Bz
In general, the sum of two vectors in n-dimensional space is obtained by adding their corresponding components.
By drawing the vectors perpendicular to each other.
By drawing the vectors one right after another.
By subtracting the numbers of the vectors magnitudes.
By adding the numbers representing the vectors magnitudes.
Which one above
To find the sum of two vectors, follow these steps:
1. Identify the two vectors you want to add together. Let's call them Vector A and Vector B.
2. Write down the components of each vector. For example, Vector A can be represented as (A₁, A₂, A₃), and Vector B as (B₁, B₂, B₃). The subscripts represent the individual components of the vectors.
3. Add the corresponding components of the vectors. For example, to find the x-component of the sum, add A₁ and B₁: A₁ + B₁. Repeat this process for the y-component and z-component.
4. Write down the sum of the components. The sum of Vector A and Vector B can be represented as (A₁ + B₁, A₂ + B₂, A₃ + B₃).
5. Simplify if necessary. If the components have common factors, you may simplify them. For example, if the x-component is 2a and the y-component is 4a, you can simplify it to 6a.
6. The resulting sum is the vector obtained by adding Vector A and Vector B.
To find the sum of two vectors, you need to combine their individual components. Here's how you can do it:
1. Identify the components: Start by identifying the components of both vectors. In a two-dimensional Cartesian coordinate system, a vector can be represented as (Ax, Ay), where Ax represents the x-component and Ay represents the y-component.
2. Add the x-components: Add the x-components of the two vectors together. This will give you the x-component of the resultant vector.
3. Add the y-components: Add the y-components of the two vectors together. This will give you the y-component of the resultant vector.
4. Combine the components: Combine the x-component and the y-component you obtained in steps 2 and 3 to form the resultant vector. The resultant vector will have the form (Rx, Ry), where Rx is the x-component and Ry is the y-component.
Note: If you are working in a three-dimensional space, you will have three components (x, y, and z), and the process is the same.
Here's an example to illustrate the process:
Vector A = (3, 2)
Vector B = (5, -1)
Sum of the vectors:
Ax + Bx = 3 + 5 = 8
Ay + By = 2 + (-1) = 1
Resultant vector = (8, 1)
So, the sum of vectors A and B is (8, 1).