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labwork [276]
3 years ago
5

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

Mathematics
1 answer:
liq [111]3 years ago
6 0

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)

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