©Zarestky
Math 151 Quiz 2 Version B
2/1/2010
NAME:_____KEY___________________________________
Section (circle one):
1.
507
508
509
510
511
512
(2 pts) Use the dot product to determine whether the pair of vectors is parallel, perpendicular, or neither.
!1,3 , 2,!5
(2)(!1) + (!5)(3) = !17 " 0
The vectors are not perpendicular.
Solve for the angle between the vectors: !1,3
2,!5 cos ! = !17
4 29 cos ! = !17
2 29 cos ! = !17
17
cos ! = !
2 29
!"0
The vectors are neither parallel nor perpendicular, i.e., neither.
Partial Credit: 0.5 points for dot product not equal to 0.
1 point for solving for theta, exact value is irrelevant.
0.5 points for a correct conclusion based on the theta, even if theta is wrong.
2.
(3 pts) Calculate the vector projection of 6,2 onto 3,4 .
proja b =
a !b
a
2
a=
6 !3+ 2 !4
(
32 + 42
)
2
3,4 =
26
78 104
3,4 =
,
25
25 25
Partial Credit: 0.5 points using the correct formula.
0.5 point for calculating b onto a instead of a onto b.
1 point for calculations
1 point for final answer (must be a vector).
(Half credit for scalar projection instead of vector projection.)
©Zarestky
3.
Math 151 Quiz 2 Version B
2/1/2010
(5 pts) x (t ) = ! t
y (t ) = 1!t
A. Complete the table of values for
the given parametric equations. Identify
any restrictions on t.
Sketch should show the left half only of
a parabola with vertex (0, 1), opening
downwards, x-intercept at x = −1
Answers may vary:
t
x
y
0
0
1
1
0
−1
4
−2
−3
9
−3
−8
16
−4
−15
t !0
B. Sketch the graph by using the ordered
pairs from part A.
C. Write the relation between x and y by
eliminating the parameter. Identify any
restrictions on x or y.
y = 1! x 2 , x ! 0
Partial Credit: 1 point for correctly completing the table.
0.5 points for the restrictions on t.
1.5 points for sketch, should match table.
1.5 points for eliminating t. No work necessary.
0.5 points for restriction on x.