I am given the following equation for the position of a particle:
${\bf r}(t) = \sin(11t)\ {\bf i} + t^4\ {\bf j} + \cos (11 t)\ {\bf k}$
I seek to:
- Find the equation of the tangent line at $t=0.2$.
- Graph the tangent line at $t=0.2$, and the path of the particle from $t=0$ to $t=2 \pi/11$ on the same graph. The line segment for the tangent line should be symmetric about the point of tangency.
I'm having trouble even declaring the vector function. I'm trying r[t_] := {Sin[11 t], t^4, Cos[11 t]}
, but I keep getting an error message. SetDelayed::write: Tag List in {0.808496,0.0016,-0.588501}[t_] is Protected. >>
So my first question would be, how do you properly define a 3D vector function?
After getting a vector function declared, how would I go about solving for $t=0.2$? Would it be as simple as r[0.2]
or would I have to use Evaluate[]
? I'm very new to the world of programming, as I'm more on the hardware side of the spectrum. Any help would be greatly appreciated.