Is this correct. Tangent lines.

[afcwestwarrior]

Homework Statement

r(t) = sin t (i) + cos t (j) + t k


Find the equation of the line tangent to r(t) at the point (0,1,0)

If you plug in 0 into to for r(t), you get (0,1,0). Thus t must equal o.

To find the vector of r' (t) or the derivative of r(t)

this equals = < cos t, - sin t, 1 > which also equals cost (i) - sin t (j) + k


So I find r'(0) = < 1,0,1>


Then my equations are

x= 1 t + 0

y = 0t + 1

z = 1t + 0


x= 1t

y = 1

z = 1t

 

[HallsofIvy]

Yes, that is correct.