I really need help with determining velocity and tangent lines from position

[reallyneedhelp]

A satellite's position at time t is x=(t, t^2, -t^3), where -infinity < t < infinity.

A. Find the velocity of the satellite at time t.
I think I have this part correct. I took the derivtive of x and plugged in t to get x'(t) at t=1 = (0, 2, -3). Correct?

B. Find the time t when the satellite's velocity is perpendicular to the plane x + y + z = 1.
I am lost here. Any help and guidance would be much appreciated.

C. Find an equation for the tangent line to the satellite's path at t=1.
Much like part B, I am stuck and don't really know where to begin.

 

[Deleted member 4993]

A satellite's position at time t is x=(t, t^2, -t^3), where -infinity < t < infinity.

A. Find the velocity of the satellite at time t.
I think I have this part correct. I took the derivtive of x and plugged in t to get x'(t) at t=1 = (0, 2, -3). Correct? ... No it should be x'(t) = (1, 2, -3)

B. Find the time t when the satellite's velocity is perpendicular to the plane x + y + z = 1.
I am lost here. Any help and guidance would be much appreciated.......................................What would be the equation of the normal to the plane? Be careful with nomenclature - you are using 'x' for two different variables!

C. Find an equation for the tangent line to the satellite's path at t=1.
Much like part B, I am stuck and don't really know where to begin.

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