Vector valued functions: finding tangent line

[bfusco]

Homework Statement

Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P

r(t)= <2sin(t), 2cos(t), 4sin²(t)>, P(1, √3, 1)

The Attempt at a Solution

I found T(t) using the formula T(t)= r'(t)/||r'(t)||

r'(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>

∴ T(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>/ 2+8sin(t)cos(t)
-note: i could do more to the denominator as far as trig functions and algebra but i don't know if it is useful.

What i don't understand is how the point is used to find the parametric equation.

 

[SammyS]

Homework Statement

Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P

r(t)= <2sin(t), 2cos(t), 4sin²(t)>, P(1, √3, 1)

The Attempt at a Solution

I found T(t) using the formula T(t)= r'(t)/||r'(t)||

r'(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>

∴ T(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>/ sqrt([STRIKE]2[/STRIKE] 4+8sin(t)cos(t))
-note: i could do more to the denominator as far as trig functions and algebra but i don't know if it is useful.

What i don't understand is how the point is used to find the parametric equation.

You have left out the square root for ||r' ||, as well as there is another error as noted above.

Do you know the general form of a parametric equation of a line in vector form?