Trying to find two vectors with known sum, what am I doing wrong?

In summary, the purpose of finding two vectors with a known sum is to solve for the individual components of the vectors that, when added together, equal the given sum. This can be useful in various mathematical and scientific applications, such as solving systems of equations or determining forces in physics. To find two vectors with a known sum, you can use a system of equations or geometric methods, such as vector addition or decomposition. Some common mistakes to avoid include forgetting to consider the direction and magnitude of the vectors, using incorrect mathematical operations, and not properly rearranging equations to solve for the unknown vectors. It is also possible to find more than two vectors with a known sum, with similar principles and methods used in physics to determine the net force on an
  • #1
Joshua G
1
1
Homework Statement
I'm trying to find two vectors whose sum is <2,0> ; where v_1 is parallel to <2,5> and v_2 is perpendicular to <2,5>.
Relevant Equations
<v1>*<v2>=0 for orthogonal
<v1>*<v2>=1 for parallel
232435-2781a2f4551da04ba35470fbf115b78a.jpg

v_1 = <-8/21,-20/21>
v_2 = <50/21,-20/21> When I take the dot product of v_2 and <2,5> I get zero, indicating they are perpendicular. Sorry for the hand writing.
 

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  • #2
Your arithmetic is off. From 5k + b = 0 you seem to have concluded that b = 5k.

In the future, please type out your work rather than attaching images.
 

Related to Trying to find two vectors with known sum, what am I doing wrong?

1. What are vectors and how are they used in mathematics?

Vectors are mathematical objects that represent direction and magnitude. They are commonly used in mathematics to represent physical quantities such as force, velocity, and acceleration.

2. How can I find two vectors that add up to a known sum?

To find two vectors with a known sum, you can use the method of vector addition. Simply set up a system of equations with the components of the two vectors and solve for the unknown components.

3. What could be causing errors in my calculations when trying to find two vectors with a known sum?

Some common errors when trying to find two vectors with a known sum include forgetting to account for negative signs, using the wrong components or units, or making a calculation mistake.

4. Is there a specific order in which I should add the vectors when trying to find their sum?

No, the order in which you add the vectors does not matter as long as you use the correct components for each vector. However, it can be helpful to add the vectors in a specific order if you are using a graphical method of vector addition.

5. How can I check if my solution for finding two vectors with a known sum is correct?

You can check your solution by using the known sum to add the components of the two vectors together. If the resulting sum matches the known sum, then your solution is correct. You can also use the Pythagorean theorem to check if the magnitude of the resulting vector matches the known sum.

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