Winter 2004 Replacement Questions MATH 200
Due: Tuesday, February 17, 2004, by 2 PM in the classroom!
Late papers will not be accepted.
Guidelines for Submission: the completed assignment should have the following
format:
(a) the problems should be done on separate sheets, single-sided,
(b) the problem statement should be given together with its solution.
(c) handwriting must be very clear.
(d) the solution should be written in complete sentences as much as possible. Partial
solutions will be given 0 credit. If only partial work is given for the solution, no credit
will be given.
(e) the assigment should be stapled.
(f) if your score on a particular problem on the test was less than 7, then you should be
the corresponding problem below. The replacement score will be scaled so the replacement
score will be 70% of the new grade for each problem. There is a cap on the total of your
new score – 85.
(h) You must sign a statement stating that all the work is your own – that
you did not copy and ask another person for help.
1. (a) Consider the vectors u=i+2 j+k,v= 2 i+j+k, and w=i+0 j+ 2 k. Let c
be a scalar. Find the value of the scalar cso that the volume of the parallelopiped
with adjacent edges cu,vand whas volume 1. Note: the edge is a scalar multiple
of unot uitself.
(b) Find the equation of the plane orthogonal to v= 2 i+j+kand contains the
point (2,3,1).
(c) Find the area of the triangle whose adjacent edges are v= 2 i+j+k, and
w=i+ 0 j+ 2 k.
2. (a) Consider the two lines given in vector form by: r1(t) = (1 + 3t)i+ (2 −t)j+tk
and r2(t) = ti+ (3 + t)j+ (1 + t)k. Find the distance between them.
(b) Consider the two lines L1given by: x= 1 −4t,y= 3 + t,z= 1 and L2given
by x= 12t−13, y= 1 + 6t, and z= 2 + 3t. Determine if these two lines intersect.
If they do, find their point of intersection.
3. Find the arc length of the curve given by r(t) = 1
2ti+1
3(1 −t)3/2j+1
3(1 + t)3/2k,
where 0 ≤t≤1.
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