Question

Determine the vector i = ∫z 1 0 r(t) dt?

Answer 1

To determine the vector i = ∫z 1 0 r(t) dt, we find that the vector i is zero.

Step-by-step explanation:

The question asks to determine the vector i = ∫z 1 0 r(t) dt. To find this vector, we need to perform an integral. Let's take a look at the given information. The position vector ř(t) from the origin to point P is ř(t) = x(t)î + y(t)ĵ + z(t)k. We can use this information to evaluate the integral.

First, we need to find the position vector r(t) = (4.0 cos 3t)i + (4.0 sin 3t)Ĵ. Since we are integrating with respect to z, we only need to consider the z component of the position vector, which is z(t) = 0.

So, the integral becomes i = ∫z 1 0 r(t) dt = ∫0 1 0 dt = 0. This means that the vector i is zero.