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Math 22 - HW #1 - Winter 11 (1604154)
Question 123456789101112131415161718192021222324252627282930
Due:Fri Jan 14 2011 11:59 PM PST
1.
Question DetailsSCalcET6 12.1.003.MI. [1387798]
Use the given points to answer the following questions.
P(1, 3, 7),
Q(-7, -2, 3),
R(0, 5, 3)
(a) Which of the points is closest to the xz-plane?
P
Q
R
(b) Which point lies in the yz-plane?
P
Q
R
Tutorial
2.
Question DetailsSCalcET6 12.1.006. [816114]
Use your knowledge of this chapter to answer the following questions.
(a) What does x = 2 represent in
2
?
a plane
nothing
a line
a point
(b) What does x = 2 represent in
3
?
nothing
a point
a plane
a line
(c) What does the equation y = 3 represent in
3
?
a line
a point
nothing
a plane
(d) What does z = 7 represent in
1 of 7
3
?
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a point
a plane
nothing
a line
(e) What does the pair of equations y = 3, z = 7 represent in
3
?
nothing
a plane
a point
a line
3.
Question DetailsSCalcET6 12.1.010. [1289313]
Find the distance from the given point to each of the following.
(2, 7, -5)
(a) the xy-plane
(b) the yz-plane
(c) the xz-plane
(d) the x-axis
(e) the y-axis
(f ) the z-axis
4.
Question DetailsSCalcET6 12.1.013.MI. [1387779]
Find an equation of the sphere determined by the given information.
passes through the point (8, 5, -1),
center (5, 6, 1)
Tutorial
5.
Question DetailsSCalcET6 12.1.016. [816217]
Write the sphere in standard form.
(x -
2 of 7
2
) + (y -
2
) + (z -
2
)=
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6.
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Question DetailsSCalcET6 12.1.021. [1289830]
Find equations of the spheres with the given center that touch the following planes.
(2, -1, 6)
(a) xy-plane
(b) yz-plane
(c) xz-plane
7.
Question DetailsSCalcET6 12.1.022. [1289781]
Find an equation of the largest sphere with the given center that is contained in the first octant.
(7, 5, 9)
8.
Question DetailsSCalcET6 12.2.007. [1047040]
Use the given points to answer the following questions.
A(2, 3),
B(-3, 2)
(a) Find a vector a with representation given by the directed line segment from A to B.
,
(b) Draw the line segment from A to B and the equivalent representation starting at the origin. (Do this on paper. Your instructor may
ask you to turn in this work.)
9.
Question DetailsSCalcET6 12.2.011. [816970]
Use the given points to answer the following questions.
A(0, 4, 3),
B(2, 4, -5)
(a) Find a vector a with representation given by the directed line segment from A to B.
,
,
(b) Draw the line segment from A to B and the equivalent representation starting at the origin. (Do this on paper. Your instructor may
ask you to turn in this work.)
10.
Question DetailsSCalcET6 12.2.013. [816144]
Use the given vectors to answer the following questions.
-3, 3,
7, -2
(a) Find the sum of the vectors.
,
(b) Illustrate geometrically. (Do this on paper. Your instructor may ask you to turn in this work.)
11.
Question DetailsSCalcET6 12.2.017. [1289004]
Find each of the following.
a=
b=
5, -12
-1, -4
(a) a + b
3 of 7
,
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(b) 4a + 5b
,
(c) | a |
(d) | a - b |
12.
Question DetailsSCalcET6 12.2.020. [1288095]
Find each of the following.
a = 4i - 4j + 4k
b = 3j - k
(a) a + b
i+
j+
k
i+
j+
k
(b) 3a + 5b
(c) | a |
(d) | a - b |
13.
Question DetailsSCalcET6 12.2.021.MI. [1386478]
Find a unit vector that has the same direction as the given vector.
-6i + 7j
Tutorial
14.
Question DetailsSCalcET6 12.2.022. [1288038]
Find a unit vector that has the same direction as the given vector.
15.
-5, 3, 3
,
,
Question DetailsSCalcET6 12.2.024. [1289492]
Find a vector that has the same direction as the given vector but has length 3.
16.
-4, 2, -2
,
,
Question 12.2.025. DetailsSCalcET6 [1289585]
If v lies in the first quadrant and makes an angle of /3 with the positive x-axis and | v | = 6, find v in component form.
i+
17.
j
Question DetailsSCalcET6 12.2.032. [816167]
Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a mass of 7 kg.
The ropes, fastened at different heights, make angles of 52 and 40 with the horizontal. Give your answers correct to two decimal places.
2
(Use g = 9.8 m/s for the acceleration due to gravity.)
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(a) Find the tension in 3 m rope.
i+
j
(ii) Find the magnitude of this tension.
N
(b) Find the tension in 5 m rope.
i+
j
(ii) Find the magnitude of this tension.
N
18.
Question DetailsSCalcET6 12.2.030. [816243]
The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45W at a speed of 50 km/h. (This
means that the direction from which the wind blows is 45 west of the northerly direction.) A pilot is steering a plane in the direction N60E
at an airspeed (speed in still air) of 150 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of
the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the
plane. Give your answers correct to one decimal place.
N
E (true course)
km/h (ground speed)
19.
Question DetailsSCalcET6 12.3.005. [808080]
Find a b.
a=
b=
20.
2, 4, 1/3
7, -3, -6
Question DetailsSCalcET6 12.3.007. [808052]
Find a b.
a = i - 4j + 5k
b = 5i + 7k
21.
Question DetailsSCalcET6 12.3.009. [1288995]
Find a b when | a | = 4, | b | = 9, and the angle between a and b is 2/3.
22.
Question DetailsSCalcET6 12.3.017. [808088]
Find the angle between the vectors. (Round your answer to the nearest degree.)
3, -1, 1
b = -3, 3, 1
a=
23.
Question DetailsSCalcET6 12.3.022. [808090]
Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
A(0, 3, 2),
B(-3, 3, 2),
C(2, 3, -2),
CAB =
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ABC =
BCA =
24.
Question DetailsSCalcET6 12.3.023. [808069]
Determine whether the given vectors are orthogonal, parallel, or neither.
(a) a =
-8, 4, 4,
b=
9, -8, 1
orthogonal
parallel
neither
(b) a =
2, 4,
b=
-2, 1
orthogonal
parallel
neither
(c) a = -i + 4j + 4k,
b = 12i + 4j - k
orthogonal
parallel
neither
(d) a = 6i + 4j - 8k,
b = -9i - 6j + 12k
orthogonal
parallel
neither
25.
Question DetailsSCalcET6 12.3.026. [808063]
For what values of b are the given vectors orthogonal?
-7, b, 3,
x=
b, b2, b
(smallest value)
x=
x=
26.
(largest value)
Question DetailsSCalcET6 12.3.027. [1289584]
Find a unit vector with a positive i component that is orthogonal to both i + j and i + k. (Express your answers in terms of i for i, j for j and
k for k.)
27.
Question DetailsSCalcET6 12.3.029. [1288268]
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.)
1, 2, 1
cos() =
cos() =
cos() =
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=
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28.
Question DetailsSCalcET6 12.3.038. [1288568]
Find the scalar and vector projections of b onto a.
a=
2, -3, 6,
b=
4, -3, 4
comp b =
a
proj b =
a
29.
,
,
Question DetailsSCalcET6 12.3.043. [1287907]
Use the given vector to find a vector b such that comp b = 3.
a
a=
s, t,
30.
4, 0, 1
Question DetailsSCalcET6 12.3.045.MI. [1386467]
Find the work done by a force F that moves an object from the point P to the point Q along a straight line. The distance is measured in
meters and the force in newtons.
F = 5i - 9j + 9k;
P = (0, 12, 4),
Q = (4, 12, 20)
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Assignment Details
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