Question

Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your answers as a comma-separated list.)

Answer 1

\[r(t)=<7\cos(t), 7\sin(t),4>\]
\[P(\frac{ 7 }{ \sqrt{2} },[\frac{ 7 }{ \sqrt{2} },4) \]
\[T(\frac{ \pi }{ 4 })=<\frac{ -\sqrt{2} }{ \sqrt{2} },\frac{ \sqrt{2} }{ 2 },0>\]

Answer 2

Just so I'm following ... \(\vec{r}(t)\) is the given curve, the point is \(\left(\dfrac{7}{\sqrt2},\dfrac{7}{\sqrt2},4\right)\), and the tangent vector at \(P\), which occurs at \(t=\dfrac{\pi}{4}\), is \(T\left(\dfrac{\pi}{4}\right)=\left\langle -\dfrac{1}{\sqrt2},\dfrac{1}{\sqrt2},0\right\rangle\).

Is that right?

Answer 3

And now you have to find the equation of the line containing \(T\), from the looks of it.

Answer 4

you know the equation of a line in vector form?

Answer 5

L(t) = P + t*v
P is a point on the line and v is a vector parallel to the line

Answer 6

@perl, \(\vec{v}\) would be \(T\), right? I haven't worked with vector calc in a while.