Quiz 6
Math 1320 - Engineering Calculus II
Name:
March 6, 2014
Quiz Score:
/??
Answer each question completely in the area below. Show all work and explain your reasoning.
If the work is at all ambiguous, it is considered incorrect. No phones, calculators, or notes are
allowed. Anyone found violating these rules will be asked to leave immediately. Point values are in
the square to the left of the question. If there are any other issues, please ask the instructor.
1. Consider the following two vectors:
u
v
Match each of the following vector expressions with their corresponding graphical vector.
2
(a) u + v.
2
(b) u − v.
(a)
(b)
2
(c) v − u
(c)
2
(d) 2u.
(d)
1 / ??
Quiz 6
Math 1320 - Engineering Calculus II
March 6, 2014
Solution: I’ll only show one solution, but the technique should give you the right idea. Consider
u + v, for instance. The general technique is to take the tail of v and attach it to the tip of u and
draw the resulting vector. Graphically, this yields:
v
u
u+v
Notice this is exactly the vector in (b). The other answers are (c), (d), (a).
2 / ??
Quiz 6
2
Math 1320 - Engineering Calculus II
March 6, 2014
2. In 3 dimensions, draw the following and state what shape it is:
x = 5.
Hint: this is not a line.
Solution: We discussed similar objects in class. For x = 5, the x component is fixed at 5 and y , z vary
freely. This is exactly the description of a plane, which can be seen below. Any real attempt at conveying
this was accepted.
10
10
5
y
0
-5
-10
5
z 0
-5
-10
10
5
0
x
-5
-10
3 / ??