A as Sum of B & C: Vector Diagrams

In summary, the conversation discusses the representation of vector addition in a graphical form and identifies the correct diagram, number 1, as the one that correctly shows "A" as the sum of "B" and "C". The conversation also clarifies that the hypotenuse has no relevance in this operation.
  • #1
Precursor
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Homework Statement


Which of the following vector diagrams represent "A" as a sum of "B" and "C". (A=B+C)

http://img402.imageshack.us/img402/94/vectorsnj3.jpg [Broken]​

Homework Equations



None that I know of.

The Attempt at a Solution



I think the answer is number 1, because A is the hypotenuse.
 
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  • #2
Consider:
How do you graphically add one vector to another?
 
  • #3
Well actually, you can add vectors graphically because the resultant vector, which in this case is the hypotenuse, is equal to the sum of both legs of the triangle.
 
  • #4
It is not the case of whether you CAN add vectors graphically together, but what that addition operation means, the relationship between the resultant vector and those two, and which of the pictures provides a correct description.

One does that, and hypotenuses (hypotenusi?, hypotena??) have nothing at all to do with it.
 

1. What is the concept of "A as Sum of B & C" in vector diagrams?

The concept of "A as Sum of B & C" in vector diagrams refers to the graphical representation of a vector, A, as the sum of two other vectors, B and C. This is commonly used in physics and engineering to represent the direction and magnitude of a resultant force or displacement.

2. How do you draw a vector diagram for "A as Sum of B & C"?

To draw a vector diagram for "A as Sum of B & C", you first need to determine the magnitude and direction of vectors A, B, and C. Then, using a ruler and protractor, you can draw the vectors to scale on a graph paper. The tip of vector A should be placed at the starting point of vector B, and the tip of vector C should be placed at the end of vector B. The resulting vector from the starting point of A to the end point of C represents the sum of A and B.

3. What is the importance of using "A as Sum of B & C" in vector diagrams?

Using "A as Sum of B & C" in vector diagrams allows for the calculation of the resultant vector, which is crucial in determining the overall magnitude and direction of a system. This is particularly useful in analyzing forces and displacements in physics and engineering problems.

4. How do you calculate the resultant vector in "A as Sum of B & C"?

To calculate the resultant vector, you can use the Pythagorean theorem to find the magnitude of the resultant vector, and trigonometric functions to determine its direction. Alternatively, you can use vector addition to add the individual components of vectors A, B, and C to find the resultant vector's components.

5. Are there any limitations to using "A as Sum of B & C" in vector diagrams?

One limitation of using "A as Sum of B & C" in vector diagrams is that it assumes the vectors are in the same plane. If the vectors are in different planes, a three-dimensional vector addition must be used. Additionally, this method may not accurately represent the actual physical system if there are other forces or factors at play that were not considered in the diagram.

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