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8/30/10 3:19 PM
Chapter 12 review (1388790)
Due:Wed Sep 1 2010 11:59 PM PDT
Question 1234567891011121314151617181920
1.
Question DetailsSCalcET6 12.3.010. [1289118]
Find a · b when | a | = 7, | b | = √14, and the angle between a and b is 45°.
2.
Question DetailsSCalcET6 12.3.009. [1288995]
Find a · b when | a | = 4, | b | = 9, and the angle between a and b is 2π/3.
3.
Question DetailsSCalcET6 12.3.023. [808069]
Determine whether the given vectors are orthogonal, parallel, or neither.
(a) a =
‹ -9,
5, 7› ,
b=
‹ 6,
-9, 2›
orthogonal
parallel
neither
(b) a =
‹ 6, 6› ,
b=
‹ -3, 3›
orthogonal
parallel
neither
(c) a = -i + 4j + 2k,
b = 14i + 4j - k
orthogonal
parallel
neither
(d) a = 2i + 4j - 8k,
b = -3i - 6j + 12k
orthogonal
parallel
neither
4.
Question DetailsSCalcET6 12.3.025. [808108]
Use vectors to decide whether the triangle with the given vertices is right angled.
P(1, -4, -2),
Q(2, -1, -4),
R(5, -3, -5)
Yes, it is right-angled.
No, it is not right-angled.
5.
Question DetailsSCalcET6 12.3.026. [808063]
For what values of b are the given vectors orthogonal?
‹ -8,
x =
b, 4› ,
‹ b,
b2 , b›
(smallest value)
x =
x =
6.
(largest value)
Question DetailsSCalcET6 12.4.011. [1288732]
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Page 1 of 4
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Find the vector, not with determinants, but by using properties of cross products.
(j - k) × (k - i)
7.
Question DetailsSCalcET6 12.4.014. [1289779]
Consider the figure below, where | u | = 2 and | v | = 3.
(a) Find | u × v |.
(b) Determine whether u × v is directed into the screen or out of the screen.
into the screen
out of the screen
8.
Question DetailsSCalcET6 12.4.016. [808077]
The figure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths are | a | = 6 and | b | = 5.
(a) Find | a × b |.
(b) Use the right-hand rule to decide whether the components of a × b are positive, negative, or 0.
?
i+
j +
?
?
k
9.
Question DetailsSCalcET6 12.4.017. [808042]
Use the given vectors to answer the following questions.
a =
‹ 2,
3, 3› ,
b=
‹ 0,
2, 1›
(a) Find a × b.
a × b=
‹
,
,
›
,
,
›
(b) Find b × a.
b× a =
‹
10.
Question DetailsSCalcET6 12.4.019.MI. [1387420]
Find two unit vectors orthogonal to both given vectors.
1, −1, 1 ,
0, 2, 2
‹
,
,
› (smaller i-value)
‹
,
,
› (larger i-value) Tutorial
11.
Question DetailsSCalcET6 12.4.027. [808102]
Find the area of the parallelogram with the given vertices.
A(-2, 1),
B(0, 2),
C(3, 0),
D(1, -1)
12.
Question DetailsSCalcET6 12.4.030. [1359610]
Consider the points below.
P(3, 1, 5),
Q(2, 3, 2),
R(4, 0, 6)
(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
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(b) Find the area of the triangle PQR.
13.
Question DetailsSCalcET6 12.4.033. [808089]
Find the volume of the parallelepiped determined by the vectors a, b, and c.
a =
‹ 4,
1, -2› ,
b=
‹ 0,
2, 3› ,
c =
‹ 6,
-3, 5›
14.
Question DetailsSCalcET6 12.4.034. [808092]
Find the volume of the parallelepiped determined by the vectors a, b, and c.
a = i + j - k,
b = i - j + k,
c = -i + j + k
15.
Question DetailsSCalcET6 12.5.011. [1289445]
Find parametric equations and symmetric equations for the line through P 0 and parallel to the given line. (P 0 corresponds to t = 0.)
P 0 = (1, -4, 3)
x + 1 = y/2 = z + 5
x =
y =
z=
=
=
16.
Question DetailsSCalcET6 12.5.010. [1289604]
Find parametric equations and symmetric equations for the line through P 0 and perpendicular to both given vectors. (P 0 corresponds to t = 0.)
P 0 = (3, 4, 0)
i + j and j + k
x =
y =
z= t
=
= z
17.
Question DetailsSCalcET6 12.5.023. [1287896]
Find an equation of the plane through the point and perpendicular to the given vector.
(6, 2, 4)
‹ -2,
1, 2›
18.
Question DetailsSCalcET6 12.5.027. [1289243]
Find an equation of the plane through the given point and parallel to the given plane.
origin
2x - y + 2z = 2
19.
Question DetailsSCalcET6 12.5.031. [1288903]
Find an equation of the plane through the given points.
(0, 1, 1),
(1, 0, 1),
(1, 1, 0)
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20.
Question DetailsSCalcET6 12.6.011. [816129]
Use traces to sketch and identify the surface. (Do this on paper. Your instructor may ask you to turn in this work.)
x = y 2 + 5z2
cone
hyperbolic paraboloid
elliptic paraboloid
hyperbolic cylinder
hyperboloid
parabolic cylinder
elliptic cylinder
ellipsoid
Assignment Details
Name (AID): Chapter 12 review (1388790)
Submissions Allowed: 5
Category: Homework
Code:
Locked: Yes
Author: Simic, Slobodan ( [email protected] )
Last Saved: Aug 26, 2010 11:01 AM PDT
Permission: Protected
Randomization: Person
Which graded: Last
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