The velocity vector of the bee is simply the rate of change of the position of the bee.
The bee is located at [tex]\mathbf{ (3,-6,10)}[/tex] at 9 seconds.
The given parameters are:
[tex]\mathbf{r'(t) = (3,-6,10)}[/tex], when t = 0
A vector is represented as:
[tex]\mathbf{r'(t) = xi + yj + zk}[/tex]
From the question, we have:
[tex]\mathbf{\int\limits^9_0 {r'(u)} \, du = 0}[/tex]
Integrate
[tex]\mathbf{r(u)|\limits^9_0 = 0}[/tex]
Expand
[tex]\mathbf{r(9) - r(0) = 0}[/tex]
Rewrite as:
[tex]\mathbf{r(9) = r(0) }[/tex]
Recall that: [tex]\mathbf{r'(t) = (3,-6,10)}[/tex]
So, we have:
[tex]\mathbf{r(9) = 3i -6j + 10k }[/tex]
Also, we have:
[tex]\mathbf{xi + yj + zk = 3i -6j + 10k }[/tex]
By comparison;
[tex]\mathbf{x = 3}[/tex]
[tex]\mathbf{y = -6}[/tex]
[tex]\mathbf{z = 10}[/tex]
So, the bee is located at [tex]\mathbf{ (3,-6,10)}[/tex] at 9 seconds.
Read more about vectors at:
https://brainly.com/question/14775501
