Project 10: Vectors

Instructions

Use Maxima to answer the following questions.

  1. Problem 10.8.6. Note: quad_qags() 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.

Additional Notes:

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.

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

)$