Show B|A| + A|B| and A|B| - B|A| are orthogonal.

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In summary, the problem is asking to show that B|A| + A|B| and A|B| - B|A| are orthogonal. This means that the two vectors make a right angle, or an angle of 90 degrees. To show this, we need to understand the dot product and how it relates to the angle between two vectors. When two vectors are orthogonal, the dot product is zero. The dot product is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The link provided explains the properties of the dot product, with (5), (6), and (7) being the most important for this problem. Finally, (1) explains why the dot product of
  • #1
Thedream63
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Homework Statement



Show that B|A| + A|B| and A|B| - B|A| are orthogonal.

Homework Equations



Orthogonal meaning at right angles
 
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  • #2


Did you try taking the dot product of the two vectors? What should it be if they are orthogonal?
 
  • #3


Yes, but I do not know what it means by orthogonal
 
  • #4


Thedream63 said:
Yes, but I do not know what it means by orthogonal

It says what it means in the problem. 'Orthogonal' means the two vectors make an angle of 90 degrees, a right angle. What does that tell you about the dot product?
 
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  • #5


That if you add the vectors it will have a Theta of 45*?
 
  • #6


Thedream63 said:
That if you add the vectors it will have a Theta of 45*?

I think we can both agree that you have no idea what you are talking about. Could you please look up 'dot product' in your textbook or anywhere else and try and figure out what it is, and what it has to do with the angle between two vectors? Then we can talk about this further.
 
  • #7


When two vectors are orthogonal it means they are perpendicular to one another (90 degrees). When you take the dot product of two vectors, if they are orthogonal the dot product is zero.
For solving this question you should keep the properties of the dot product in mind.
Here is a link to help you out:
http://www.programmedlessons.org/VectorLessons/vch07/vch07_8.html

The ones that will be most important for you are (5), (6), (7).
(1) explains why the dot product of two orthogonal vectors is zero, since cos(90) = 0.

Hope this helps.
 
  • #8


Yes i am confused and thanks to the both of you.
 

FAQ: Show B|A| + A|B| and A|B| - B|A| are orthogonal.

What does "Show B|A| + A|B| and A|B| - B|A| are orthogonal" mean?

This statement refers to a mathematical equation that involves the operations of taking the absolute value of a matrix and then adding or subtracting it from another matrix. The equation suggests that the resulting matrices will be orthogonal, meaning they are perpendicular and have a dot product of zero.

How is this equation relevant to science?

Orthogonality is a fundamental concept in many branches of science, including physics, engineering, and computer science. It is used to describe relationships between different variables and to solve problems involving multiple dimensions. This equation can be applied in various fields to find solutions or make predictions.

Can you provide an example of this equation in action?

Sure! Let's say we have two matrices, A and B, with the following values:

A = [1, 2, 3] and B = [4, 5, 6]

Using the equation B|A| + A|B|, we can calculate the absolute values of both matrices and then add them together, resulting in the following matrix:

ABS(B) = [4, 5, 6] and ABS(A) = [1, 2, 3]

B|A| = [4, 10, 18] and A|B| = [4, 10, 18]

Adding these two matrices together, we get [8, 20, 36]. This resulting matrix is orthogonal to the original matrices A and B.

What is the significance of orthogonal matrices in science?

Orthogonal matrices have many important properties, such as preserving angles and distances, and can be used to simplify complex calculations. In science, they are often used to represent rotations, reflections, and other transformations. They are also used in data analysis and signal processing to reduce noise and improve accuracy.

Are there any real-world applications of this equation?

Yes, there are many real-world applications of this equation. For example, it can be used in computer graphics to create 3D animations, in physics to model the behavior of particles, and in navigation systems to determine the position of objects in space. It is also used in statistics to analyze data and identify patterns.

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