Question

Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z).

Answer 1

Answer:

a) $c'(t) = (2 Cos(t), -2 Sin(t), 9e^t)$

b) $c'(t) = (2 Cos(t), -2 Sin(t), 9e^t)$

Step-by-step explanation:

We are given in the question:

$c(t) = (2 Sin(t), 2 Cos(t), 9e^t)$

F(x,y,z) = (y, -x, z)  

a) $c'(t)$

We differentiate with respect to t.

$c'(t) = (2 Cos(t), -2 Sin(t), 9e^t)$

b) F(c(t))

This is a composite function.

$F(c(t)) = F(2 Sin(t), 2 Cos(t), 9e^t)$

$= (2 Cos(t), -2 Sin(t), 9e^t)$