Dot product of two vectors

In summary: So in this case, the projection is not zero.In summary, the conversation discusses the projection of two vectors A and B, with A being (1,0) and B being (-1,0). The speaker initially states that the projection should be zero, but is actually -1, and asks where they are going wrong. Another speaker clarifies that the projection and dot product are only zero when the vectors are perpendicular, and in this case, the vectors are in opposite directions. The conversation ends with the initial speaker seeking further clarification on the concept of dot product and projections.
  • #1
amaresh92
163
0
greetings,
consider two vector as it is A(1,0) and B(-1,0). now if we find the projection of A on B we should get zero but its coming -1.where i am going wrong?
advanced thanks.
 
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  • #2
What's the condition for dot products to be zero?
 
  • #3
Hi amaresh92! :smile:

You're not going wrong.
The projection is not supposed to come out as zero, since the vectors are opposite.

Repeating Ibix, do you know what it means if the projection is zero?
 
  • #4
I like Serena said:
Hi amaresh92! :smile:
Repeating Ibix, do you know what it means if the projection is zero?

what i have understood is we find projection of one vector to another when we need to find the magnitude of one vector in the direction given by another vector.

if its wrong then what is dot product and projections are ?

any help will be appreciated
thanks
 
  • #5
Your understanding appears to be correct. Your application to this particular problem is wrong.

Your vector A points due East. Which way is B pointing? How far in an easterly direction is that, ignoring any northerly or southerly motion?
 
  • #6
The dot product and projection are zero if and only if the vectors are perpendicular.

Opposite vectors are not perpendicular - they are in the same (but opposite) direction.
 

What is the dot product of two vectors?

The dot product of two vectors is a mathematical operation that results in a scalar value. It is also known as the inner product or scalar product. It is calculated by multiplying the corresponding components of the two vectors and then adding the products together.

How is the dot product calculated?

To calculate the dot product of two vectors, you multiply the x components of the vectors, then the y components, and then the z components. Finally, add the three products together to get the dot product.

What is the purpose of the dot product?

The dot product has several important applications in mathematics and science. It is used in vector calculus, mechanics, and physics to calculate work, power, and projections. It is also used in computer graphics and machine learning for tasks such as image processing and pattern recognition.

What is the significance of the dot product value?

The value of the dot product can provide important information about the relationship between two vectors. If the dot product is zero, it means the vectors are perpendicular or orthogonal to each other. If the dot product is positive, it means the vectors are in the same direction, and if it is negative, they are in opposite directions.

Can the dot product be negative?

Yes, the dot product can be negative. This indicates that the two vectors are pointing in opposite directions. It is important to note that the magnitude of the dot product is more significant than its sign, as it provides information about the angle and relationship between the two vectors.

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