Show that the given curve c(t) is a flow line of the given velocity vector field f(x, y, z).
c(t) = (t^2, 2t − 6, 3sqrt( t > 0; f(x, y,z) = ( y+6, 2, 9/2z)
c'(t) = ?
f(c(t)) = ?

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:

Now, we evaluate the following:

Now, we have to evaluate:

When F(c(t)) = c'(t), then c(t) is a flow line of given velocity vector field F(x, y, z).

Since, , we can say that c(t) is a flow line of given velocity vector field F(x, y, z).