Vector Addition Homework: Multiplying Vectors & Gaussian Elimination

In summary, the conversation discusses how 1 1 1 can be changed to 3 3 3 through Gaussian elimination. There is confusion about whether one can multiply a vector by any number and if both vectors are being multiplied by 3 to simplify the arithmetic. The conversation also mentions that there is nothing wrong with the equation (1 1 1) = (\frac{3}{3} \frac{3}{3} \frac{3}{3}) = \frac{1}{3}(3 3 3).
  • #1
g.lemaitre
267
2

Homework Statement


Screenshot2012-07-14at25427AM.png

Homework Equations


The Attempt at a Solution


Do you see how 1 1 1 changes to 3 3 3. i know why gaussian elimination you can change any vector by multiplying it by anything you want. but for some reason i have difficulty believing that you're allowed to do that here. is that what they're doing? just multiplying that vector by 3 so as to facilitate the arithmetic. Or maybe they're multiplying both vectors by 3, so as to get rid of the 1/3, but that doesn't explain how the 1/3 gets on the left side of the parentheses.
 
Physics news on Phys.org
  • #2
There is nothing wrong with

(1 1 1) = ([itex]\frac{3}{3}[/itex] [itex]\frac{3}{3}[/itex] [itex]\frac{3}{3}) = [/itex][itex]\frac{1}{3}[/itex](3 3 3)
 
  • #3
ok, thanks
 

FAQ: Vector Addition Homework: Multiplying Vectors & Gaussian Elimination

What is vector addition?

Vector addition is the process of combining two or more vectors to create a new vector. It involves adding the corresponding components of each vector together to form the components of the new vector. This process is used in physics and engineering to calculate the overall force or displacement of multiple vectors acting on an object.

How do you multiply vectors?

Vectors can be multiplied in two ways: scalar multiplication and vector multiplication. Scalar multiplication involves multiplying a vector by a scalar (a single number) to change its magnitude. Vector multiplication, on the other hand, can take the form of dot product or cross product, and it results in a new vector with different properties.

What is Gaussian elimination?

Gaussian elimination is a method used to solve systems of linear equations. It involves using elementary row operations (such as swapping rows, multiplying rows by a constant, and adding rows together) to transform a system of equations into a simpler form that is easier to solve. This process is often used in mathematics and engineering to solve complex systems of equations.

How is vector addition used in real-world applications?

Vector addition is used in many real-world applications, such as navigation systems, physics problems, and computer graphics. In navigation, vector addition is used to calculate the overall displacement of an object by combining the different velocities or forces acting on it. In physics, vector addition is used to calculate the resultant force or displacement of multiple vectors acting on an object. In computer graphics, vector addition is used to manipulate the position, size, and orientation of objects in a 3D space.

What are some common mistakes when performing vector addition?

Some common mistakes when performing vector addition include forgetting to account for the direction of the vectors, miscalculating the magnitude of the resulting vector, and using the wrong type of vector multiplication. It is important to carefully label and draw the vectors, and to use the correct formulas for scalar and vector multiplication in order to avoid these errors.

Similar threads

Replies
4
Views
2K
Replies
8
Views
1K
Replies
9
Views
4K
Replies
5
Views
1K
Replies
10
Views
1K
Replies
16
Views
2K
Replies
4
Views
1K
Back
Top