Project 10: Vectors

Instructions

Use Maxima to answer the following questions.

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

Notes

You will need to load() the "vect" and "draw" packages.
You may want to define some functions like Cross(), Norm(), and Unit() to make your life easier.

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,
    head_length=0.05,
    dimensions=[400,400],
    view=[34,57]
)$

draw3d(
    color=red,Tvec,Tlabel,
    color=dark_green,Nvec,Nlabel,
    color=orange,Bvec,Blabel,
    color=blue,curve,point
)$