Question about vectors and dot product.

[teeeeee]

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 $$\int \frac{d}{dt} (A) dV$$

equal to: $$\frac{d}{dt} \int (A) dV$$

Thank you

 

[elibj123]

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.