Vector fields, flow lines question. Seems simple but I'm stuck

Ben cunnington

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Consider the vector field F(x,y,z) = ax i + by j + cz k where F, i, j, k are vectors


Let c(t) = (x(t), y(t), z(t)) be the flow line such that c(0)= (x_0, y_0, z_0). Find c(t) for all t. Note: c is a vector and x_0 represents a constant, like those x's with the 0's on the bottom right hand corner.


I know that if c(t) is a flow line then c'(t) = F( c(t) ) but I have no idea what this question is actually asking for. Thanks in advance for any help/tips.

Edit: I think I'm supposed to solve the differential equation c'(t) but I'm at a dead end given that c(t) is actually given.
Edit: Sorry, again. I've added the "Find"
 
Last edited:
Consider the vector field $\tilde{F}(x,y,z) = ax \tilde{i} + by \tilde{j} + cz\tilde{k}$


Let $\tilde{c}(t) = (x(t), y(t), z(t))$ be the flow line such that $\tilde{c}(0)= (x_0, y_0, z_0)$. Find $\tilde{c}(t)$ for all $t$.


I know that if $\tilde{c}(t)$ is a flow line then $\tilde{c}'(t) = \tilde{F}(\tilde{c}(t))$ but I have no idea what this question is actually asking for. Thanks in advance for any help/tips.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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Consider the vector field F(x,y,z) = ax i + by j + cz k where F, i, j, k are vectors


Let c(t) = (x(t), y(t), z(t)) be the flow line such that c(0)= (x_0, y_0, z_0). c(t) for all t.

Note: c is a vector and x_0 represents a constant, like those x's with the 0's on the bottom right hand corner.


I know that if c(t) is a flow line then c'(t) = F( c(t) ) but I have no idea what this question is actually asking for. Thanks in advance for any help/tips.

Edit: I think I'm supposed to solve the differential equation c'(t) but I'm at a dead end given that c(t) is actually given.

Read your post again!!

I do not see a question !!

I see "let", I see "consider" - but I do not see any "What" or "Determine" or "Find" or some such instruction!!!
 
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