Project 10: Vectors

Instructions

Use Maxima to answer the following questions.

  1. Problem 10.8.6. Note: romberg() is the numeric version of integrate()
  2. Problem 10.8.30
  3. Problem 10.8.39. In addition, graph the curve and the T, N, and B vectors at the indicated point.

Notes

Maxima

Here is some example code for making the graph with the TNB frame. Some values are labeled before it gets to this point; you can't run this directly. Use wxdraw3d() instead of draw3d() to embed the graph inside the Maxima file.

R: /* vector curve */$
r0: /* vector containing initial value */$

Tvec:vector(r0,T0)$
Nvec:vector(r0,N0)$
Bvec:vector(r0,B0)$
curve:parametric(r[1],r[2],r[3],t,t0-0.2,t0+0.2)$
point:points([r0])$
Tlabel:label(append(["T"],r0+1.1*T0))$
Nlabel:label(append(["N"],r0+1.1*N0))$
Blabel:label(append(["B"],r0+1.1*B0))$
 
set_draw_defaults(
    xrange=[2,4],yrange=[1,3],zrange=[1,3],
    line_width=2,grid=true,xyplane=1,
    point_size=1.5,point_type=filled_circle,
    dimensions=[400,400],
    view=[34,57]
)$
 
draw3d(
    color=red,Tvec,Tlabel,
    color=dark_green,Nvec,Nlabel,
    color=orange,Bvec,Blabel,
    color=blue,curve,point
)$