HW05 – gilbert – (55035)
1
This print-out should have 10 questions.
Multiple-choice questions may continue
on the next column or page – find all
choices before answering.
−→
express AQ in terms of u and v.
−→
1
1.
AQ
=
2
u − v
001
0.0 points
Which, if any, of the following
−−→
A.
−QP ,
B.
P Q ,
are representations of vectors when P, Q
are points in 3-space?
1. both of them
2. neither of them
3. A only correct
4. B only
Explanation:
−−→
A. TRUE: −QP is the displacement vector
having initial point P and terminal point Q.
B. FALSE: P Q is the line segment
from P to Q.
keywords: vectors, scalars, T/F, line
segment, displacement vector, length
002
0.0 points
When u, v are the displacement vectors
−→ −→ u = AP , v =
AC ,
determined by the parallelogram
R
Q
P
S
O
C
B
A
2.
−→
AQ
=
u
+
1
2
v correct
3.
−→
AQ
=
1
2
u
+
v
1
4.
−→
AQ
=
−
2
v
1
5.
−→
AQ
=
−
2
u
1
6.
−→
AQ
=
2
v
−
u
Explanation:
By the parallelogram law for the
addition of vectors we see that
−→
1
AQ
=
u +
2
v
.
003
0.0 points
Find the vector v
having a representation
−−→
by the directed line segment AB with
respect to points A(3, −1) and B(−4, 3).
1. v
=
h−7, 4O correct
2. v
=
h−1, 2O
3. v
=
h−7, −4O
4. v
=
h1, 2O
5. v
=
h7, 4O
6. v
=
h−1, −2O
Explanation:
Since
−−→
AB
=
h−4 − 3, 3 + 1O ,
we see that
v
=
h−7, 4O
.