Question

Find a unit tangent vector to the curve *r = 3 cos 3t
i + 3 sin 2t j* at

Answer #1

Find the unit tangent vector T and the principle unit normal
vector N of ⃗r(t) = cos t⃗i + sin t⃗j + ln(cos t)⃗k at t = π .

6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3 + 1 2 t
2 i (a) Find r 0 (t) (b) Find the unit tangent vector to the space
curve of r(t) at t = 3. (c) Find the vector equation of the tangent
line to the curve at t = 3

Given r(t) = (et cos(t) )i + (et sin(t) )j
+ 2k. Find
(i) unit tangent vector T.
(ii) principal unit normal vector N.

Find the unit tangent vector T(t) and the curvature κ(t) for the
curve r(t) = <6t^3 , t, −3t^2 >.

20. Find the unit tangent vector T(t) and then use it to find a
set of parametric equations for the line tangent to the space curve
given below at the given point.
r(t)= -5t i+ 2t^2 j+3tk, t=5

Find the derivative r '(t) of the
vector function r(t).
<t cos 3t , t2, t sin 3t>

Given that the acceleration vector is a ( t ) = (−9 cos( 3t ) )
i + ( −9 sin( 3t ) ) j + ( −5 t ) k, the initial velocity is v ( 0
) = i + k, and the initial position vector is r ( 0 ) = i +j + k,
compute: the velocity vector and position vector.

Given that the acceleration vector is a(t)=(-9 cos(3t))i+(-9
sin(3t))j+(-5t)k, the initial velocity is v(0)=i+k, and the initial
position vector is r(0)=i+j+k, compute:
A. The velocity vector v(t)
B. The position vector r(t)

6) please show steps and explanation.
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the area of the triangle
PQR.

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

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