Respuesta :
Answer:
The given curve c(t) is a is a flow line of given velocity vector field F(x, y, z).
Step-by-step explanation:
We are given the following information in the question:
[tex]c(t) = (t^2, 2t-6, 3\sqrt{t}), t > 0\\\\ F(x, y, z) =(y+6, 2, \frac{9}{2z} )[/tex]
Now, we evaluate the following:
[tex]c'(t) = \frac{d(c(t))}{dt} = (2t, 2, \frac{3}{2\sqrt{t}} )[/tex]
Now, we have to evaluate:
[tex]F(c(t)) = (2t-6+6, 2, \frac{9}{6\sqrt{t}} ) = (2t, 2, \frac{3}{2\sqrt{t}} )[/tex]
When F(c(t)) = c'(t), then c(t) is a flow line of given velocity vector field F(x, y, z).
Since, [tex]F(c(t)) = c'(t)[/tex], we can say that c(t) is a flow line of given velocity vector field F(x, y, z).
