Question about vectors and dot product.

In summary, the conversation discusses whether -E dotted with (A + B) is equal to -E.A -E.B, and also if \int \frac{d}{dt} (A) dV is equal to \frac{d}{dt} \int (A) dV. The answer to both questions is yes, as long as certain "nice" conditions are met.
  • #1
teeeeee
14
0
Hi,
Can someone tell me if: -E dotted with ( A + B )

is equal to -E.A -E.B where E, A and B are all vectors

What I mean is, does the minus sign appear on the E.B bit as well?


Also, is [tex]\int \frac{d}{dt} (A) dV[/tex]

equal to: [tex]\frac{d}{dt} \int (A) dV[/tex]

Thank you
 
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  • #2
1) Yes off course.

2) Usually the conditions are for all to be "nice": A must be differentiable wrt to t at every point in V, the former integral must converge in order for it to be equal to the latter. I guess you are working with such a "nice" field and volume V, so in that case you may switch differentiation and integration.
 

Related to Question about vectors and dot product.

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is often represented by an arrow pointing in the direction of the vector, with its length representing the magnitude.

2. What is the dot product of two vectors?

The dot product of two vectors is a mathematical operation that results in a scalar (single value) by multiplying the magnitudes of the two vectors and the cosine of the angle between them.

3. How is the dot product calculated?

To calculate the dot product of two vectors, you multiply the corresponding components of the two vectors and then add the products. For example, if vector A = [a1, a2, a3] and vector B = [b1, b2, b3], then the dot product is a1*b1 + a2*b2 + a3*b3.

4. What is the purpose of the dot product?

The dot product has a variety of applications in mathematics and science, including calculating the angle between two vectors, finding the projection of one vector onto another, and determining the work done by a force on an object.

5. How is the dot product related to the cosine of the angle between two vectors?

The dot product is equal to the product of the magnitudes of the two vectors multiplied by the cosine of the angle between them. This relationship is often used to find the angle between two vectors when given their dot product and magnitudes.

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