Writing Vector <1,7> as Sum of 2 Vectors

In summary, writing a given vector as a sum of two other vectors is a useful technique in vector manipulation and simplifying equations. It allows for easier calculation and analysis of vector quantities, as well as breaking down complex vectors into simpler components. This can be done using various methods such as trial and error or vector algebra techniques. There are infinite ways to write a vector as a sum of two vectors, but some may be more useful or simpler than others. Additionally, a vector can also be written as a sum of more than two vectors, but it is often preferred to express it as a sum of only two vectors for simplicity.
  • #1
Loppyfoot
194
0

Homework Statement



Write the vector <1,7> as a sum of two vectors, one parallel to <2,-1> and one perpendicular to <2,-1>

Homework Equations


DOt Product


The Attempt at a Solution



I'm confused on where to begin this problem. Should I be using the dot product?

Thanks
 
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  • #2
i think you should draw out the vectors as they make up a right angle triangle.
 
  • #3
I got the answer:

<-2,1> and <3,6>
 

1. What is the meaning of "Writing Vector <1,7> as Sum of 2 Vectors"?

Writing Vector <1,7> as Sum of 2 Vectors refers to the process of expressing a given vector in the form of a sum of two other vectors. This is a common technique used in vector manipulation and can be helpful in simplifying complex vector equations.

2. Why is it important to be able to write a vector as a sum of two vectors?

Writing a vector as a sum of two vectors allows for easier manipulation and calculation of vector quantities. It also helps in breaking down a complex vector into simpler components, making it easier to understand and analyze.

3. How do you write Vector <1,7> as a sum of two vectors?

To write Vector <1,7> as a sum of two vectors, we need to find two vectors whose sum will result in <1,7>. This can be done by trial and error or by using vector algebra techniques such as solving systems of equations or using vector decomposition methods.

4. Is there a unique way to write a vector as a sum of two vectors?

No, there are infinite ways to write a vector as a sum of two vectors. This is because there are many possible combinations of vectors that can result in the same vector when added together. However, some combinations may be more useful or simpler than others.

5. Can a vector be written as a sum of more than two vectors?

Yes, a vector can be written as a sum of any number of vectors. This is known as vector decomposition and is a common technique in vector analysis. However, for simplicity, it is often preferred to express a vector as a sum of only two vectors.

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