Solving for Vector w in R3 Homework Problem

In summary, to solve for vector w in R3, you need to use the properties and operations of vectors in three-dimensional space, such as addition, subtraction, scalar multiplication, and vector cross product. A calculator can be used for these calculations, but it is important to understand the concepts behind them. The key steps for solving for vector w in R3 include setting up equations, applying operations, and solving for unknown components. To check for accuracy, you can plug in values and compare with alternative methods. Common mistakes to avoid include using incorrect operations, setting up equations incorrectly, and making calculation errors. Double checking work and having a good understanding of vector properties can help avoid these mistakes.
  • #1
Computnik
12
0

Homework Statement


Hi, I have a really short (and dumb) question.

In one of my homework problems they talk about a vector w, such that w=e1+e2+e3. (In R3.)

The Attempt at a Solution


I guess they mean that: e1=(1,0,0), e2=(0,1,0) and e3=(0,0,1). So w=(1,1,1). Right?
 
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  • #2
Sort of. the ei are usually basis vectors, but they do not have to be Cartesian basis vectors.
Any three orthogonal vectors will do - helps if they are orthonormal.
 
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1. How do I approach solving for vector w in R3?

To solve for vector w in R3, you need to use the properties and operations of vectors in three-dimensional space. This includes addition, subtraction, scalar multiplication, and vector cross product.

2. Can I use a calculator to solve for vector w in R3?

Yes, you can use a calculator to perform the necessary calculations for solving for vector w in R3. However, it is important to understand the concepts behind the calculations in order to accurately interpret the results.

3. What are the key steps for solving for vector w in R3?

The key steps for solving for vector w in R3 include setting up the equations using vector components, applying the appropriate operations, and solving for the unknown components of vector w.

4. How do I know if my solution for vector w in R3 is correct?

You can check if your solution for vector w in R3 is correct by plugging in the values for the unknown components into the original equations and seeing if they satisfy the equations. Additionally, you can compare your solution with alternative methods, such as using a calculator or software.

5. What are some common mistakes to avoid when solving for vector w in R3?

Some common mistakes to avoid when solving for vector w in R3 include forgetting to use the correct operations, incorrectly setting up the equations, and making errors in calculations. It is important to double check your work and be familiar with the properties and operations of vectors in R3 to avoid these mistakes.

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