Surgent MAT 267 ONLINE A Spring 2019
Assignment Midterm 1 due 01/22/2019 MST
Problem 1.
2. (1 point) Find a vector athat has the same direction as
h−8,9,8ibut has length 4.
Answer: a=
Answer(s) submitted:
•<-2.213,2.490,2.213>
(correct)
Problem 2.
4. (1 point)
Perform the following operations on the vectors ~u=
h−5,−1,−3i,~v=h−2,−1,0i, and ~w=h−5,−1,0i.
~u·~w=
(~u·~v)~u=
((~w·~w)~u)·~u=
~u·~v+~v·~w=
Answer(s) submitted:
•26
•<-55,-11,-33>
•910
•22
(correct)
Problem 3.
10. (1 point) Given that the acceleration vector is a(t) =
(−9cos(−3t))i+ (−9sin(−3t))j+ (2t)k, the initial velocity is
v(0) = i+k, and the initial position vector is r(0) = i+j+k,
compute:
A. The velocity vector v(t) = i+j+
k
B. The position vector r(t) = i+j+
k
Answer(s) submitted:
•3sin(-3t)+1
•-3cos(-3t)+3
•((2tˆ2)/2)+1
•-sin(-3t+t)
•sin(-3t)+3t+1
•((2tˆ3)/6)+t+1
(score 0.833333333333333)
Problem 4.
9. (1 point) Find the length of the given curve:
r(t) = h5t,−4sint,−4costi
where −4≤t≤1.
Answer(s) submitted:
•32.0156
(correct)
Problem 5.
1. (1 point) Find the equation of the sphere if one of its di-
ameters has endpoints (2,−3,−3)and (3,−1,0).
= 0.
Answer(s) submitted:
•xˆ2+yˆ2+zˆ2-5x+4y+3z+9
(correct)
Problem 6.
3. (1 point) Find the following expressions using the graph
below of vectors u,v, and w.
1. u +v=
2. 2u+w=
3. 3v−6w=
4. |w|=
Note: You can click on the graph to enlarge the image.
Answer(s) submitted:
•2i+7j
•10i+7j
•-27i+18j
•sqrt(17)
(score 0.75)
Problem 7.
6. (1 point) Find the area of the triangle with vertices:
Q(−2,2,3),R(1,1,1),S(0,5,1).
Answer(s) submitted:
•(1/2)sqrt(189)
(correct)
1
Problem 8.
7. (1 point) Find an equation of a plane containing the three
points A= (−4,−2,1),B= (−2,0,−4),C= (−2,1,−2)
.
Answer(s) submitted:
•9x-4y+2z=0
(incorrect)
Problem 9.
8. (1 point) Find parametric equations for the tangent line at
the point
cos5
6π,sin5
6π,5
6πon the curve x=cost,y=sint,z=t
x(t)=
y(t)=
z(t)=
(Your line should be parametrized so that it passes through
the given point at t=0).
Answer(s) submitted:
•-(sqrt(3)+t)/2
•(1-sqrt(3)t)/2
•(5pi)/(6)+t
(correct)
Problem 10.
5. (1 point)
Several unit vectors ~r,~
s,~
t,~u,~n,and ~ein the xy-plane
(not three-dimensional space) are shown in the figure.
Using the geometric definition of the dot product, are
the following dot products positive, negative, or zero?
You may assume that angles that look the same are the
same.
? 1. ~
t·~u
? 2. ~
s·~
t
? 3. ~e·~r
? 4. ~r·~
s
? 5. ~e·~
s
? 6. ~r·~u
? 7. ~n·~e
? 8. ~n·~
t
(Click on graph to enlarge)
Answer(s) submitted:
•Positive
•Positive
•Negative
•Positive
•Zero
•Negative
•Zero
•Negative
(correct)
Generated by c
WeBWorK, http://webwork.maa.org, Mathematical Association of America
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