Maple #4 is due Monday 7 Feb 2000

For FULL credit STAPLE your sheets together.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Each plot must be rotated to a "nice" position and "look good (smooth)"
. Each plot must have include axes and the title must include your name
and what was plotted. Note that the expressions below are not
necessarily in a form that Maple likes. Be sure to answer the questions
in #3.

1. Use "arrow(s)" to illustrate how the vector addition is commutative,
that is u + v is the same as v + u. (Pick u = <2, 4> and v= <5, 1>
and draw 5 arrows: u, v starting at the end of u, u+v, v, and u starting
at the end of v.  [hint: with(plottools) and display.]
2. Plot the plane P with equation, 3x-2y+5z = 12 and an normal to P
on the same plot. Have the normal plotted as an arrow with its base
at the point on the plane nearest the origin.
3. The following function is from a Matlab demo.
f(x,y)= 3(1-x)^2 e^(-x^2-(y+1)^2)
    - 10(x/5-x^3-y^5)e^(-x^2-y^2) -(1/3)e^(-(x+1)^2-y^2).
[Remember, either define e:=exp(1) or replace e^x with exp(x). A common
error is to replace e^x with exp^x, and unfortunately Maple doesn't
notice the error, and does something dumb.] Have Maple find
the both partials of f, f_x and f_y [Read f_x as f sub x.] and all
four second partials of f, f_xx, f_xy, f_yx and f_yy.] [Hint let
F:=be the expression for the function, and just do diff(F,...)]
Is f_xy = f_yx?
4. Using the matlab demo function, draw the graph together with 
the two curves we get when we hold x = the constant 1/5 and when we
hold y = the constant 3/2. [This time define F to be the "Maple"
function F:=(x,y)->ugly expression. (NOTE not F(x,y):= ugly expression.)
and do spacecurves [1/5,y,F(1/5),y],y=-3..3 and [x,3/2,F(x,3/2)],x=-3..3
with large thickness.]
5. Use Maple to find the projection of the vector u in the v direction.
Do the calculation once with u:=vector([1,2,3]) and v:=vector([3,1,3])
and once with u:=vector([u1,u2,u3]);v:=vector([v1,v2,v3]). [Hint
remember norm is norm(v,2).]