Vectors using the component method

In summary, the component method for vectors is a mathematical approach for breaking down a vector into its horizontal and vertical components. This method can be used for any type of vector and is useful for solving problems involving vector addition, subtraction, and multiplication. To find the components of a vector using this method, you need to know the magnitude and direction of the vector and use trigonometric functions to calculate the horizontal and vertical components. The component method can also be applied to vectors in three dimensions, where you would need to find the horizontal, vertical, and depth components. The difference between the component method and the graphical method is that the former involves mathematical calculations while the latter involves using geometric principles.
  • #1
farhana21
7
0
Use the component method to add the vectors and shown in the figure. The length of is 2.55 m and the angle θ = 31.5°. Express the resultant + in unit-vector notation.

The answer should be in the form of ...i + ...j

so far i have done

3*cos(31.5) = 2.56 so this is for ...i but I am unsure of how to find vector j for the y axis.

Please could someone advise me. All help and guidance given is much appreciated

vector.gif
 
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  • #2
may the sin() be with you.
 

1. What is the component method for vectors?

The component method for vectors is a mathematical approach for breaking down a vector into its horizontal and vertical components. This method is useful for solving problems involving vector addition, subtraction, and multiplication.

2. How do you find the components of a vector using the component method?

To find the components of a vector using the component method, you first need to know the magnitude and direction of the vector. Then, you can use trigonometric functions (such as sine and cosine) to calculate the horizontal and vertical components of the vector.

3. Can you use the component method for vectors in three dimensions?

Yes, the component method can be used for vectors in three dimensions. In this case, you would need to find the horizontal, vertical, and depth components of the vector using trigonometric functions and the vector's magnitude and direction.

4. What is the difference between the component method and the graphical method for vectors?

The component method involves breaking down a vector into its components and using mathematical calculations to solve problems. The graphical method, on the other hand, involves drawing the vectors on a graph and using geometric principles to solve problems.

5. Can the component method be used for any type of vector?

Yes, the component method can be used for any type of vector, including displacement, velocity, and force. It is a versatile method that can be applied to a wide range of vector problems.

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