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mathematics
precalculus

Precalculus 9th edition Michael Sullivan - Solutions

Find the equation of a sphere with radius r and center P0.r = 2; P0 = (1,2,2)
Find the equation of a sphere with radius r and center P0.r = 1; P0 = (3,1,1)
In space, the collection of all points that are the same distance from some fixed point is called a sphere. See the illustration. The constant distance is called the radius, and the fixed point is the center of the sphere. Show that the equation of a sphere with center at (x0,y0,z0) and radius r
Consider the double-jointed robotic arm shown in the figure. Let the lower arm be modeled by a = (2,3,4) the middle arm be modeled by b = (1, -1, 3) and the upper arm by c = (4,-1,-2) where units are in feet. (a) Find a vector d that represents the position of the hand. (b)
Find the direction angles of each vector. Write each vector in the form of equation (7).v = 2i + 3j - 4k M[(cos a)i + (cos B)j + (cos y)k] (7)
Find the direction angles of each vector. Write each vector in the form of equation (7).v = 3i - 5j + 2k M[(cos a)i + (cos B)j + (cos y)k] (7)
Find the direction angles of each vector. Write each vector in the form of equation (7).v = j + k = ||M[(cos a)i + (cos B)j + (cos y)k] (7) V
Find the direction angles of each vector. Write each vector in the form of equation (7).v = i + j M[(cos a)i + (cos B)j + (cos y)k] (7)
Find the direction angles of each vector. Write each vector in the form of equation (7).v = i - j - k M[(cos a)i + (cos B)j + (cos y)k] (7)
Find the direction angles of each vector. Write each vector in the form of equation (7).v = i + j + k M[(cos a)i + (cos B)j + (cos y)k] (7)
Find the direction angles of each vector. Write each vector in the form of equation (7).v = -6i + 12j + 4k
Find the direction angles of each vector. Write each vector in the form of equation (7).v = 3i - 6j - 2k
Find the dot product v.w and the angle between v and w. v = 3i - 4j + k, w = 6i - 8j + 2k
Find the dot product v.w and the angle between v and w. v = 3i + 4j + k, w = 6i + 8j + 2k
Find the dot product v.w and the angle between v and w. v = i + 3j + 2k, w = i - j + k
Find the dot product v.w and the angle between v and w. v = 3i - j + 2k, w = i + j - k
Find the dot product v.w and the angle between v and w. v = 2i + 2j - k, w = i + 2j + 3k
Find the dot product v.w and the angle between v and w. v = 2i + j - 3k, w = i + 2j + 2k
Find the dot product v.w and the angle between v and w. v = i + j, w = -i + j - k
Find the dot product v.w and the angle between v and w. v = i - j, w = i + j + k
Find the unit vector in the same direction as v. v = 2i - j + k
Find the unit vector in the same direction as v. v = i + j + k
Find the unit vector in the same direction as v. v = -6i + 12j + 4k
Find the unit vector in the same direction as v. v = 3i - 6j - 2k
Find the unit vector in the same direction as v. v = -3j
Find the unit vector in the same direction as v. v = 5i
Find each quantity if and v = 3i - 5j + 2k and w = -2i + 3j - 2k. |v | + |w|
Find each quantity if and v = 3i - 5j + 2k and w = -2i + 3j - 2k. |v| - |w|
Find each quantity if and v = 3i - 5j + 2k and w = -2i + 3j - 2k. |v + w|
Find each quantity if and v = 3i - 5j + 2k and w = -2i + 3j - 2k. |v - w|
Find each quantity if and v = 3i - 5j + 2k and w = -2i + 3j - 2k. 3v - 2w
Find each quantity if and v = 3i - 5j + 2k and w = -2i + 3j - 2k. 2v + 3w
Find |v|. v = 6i + 2j - 2k
Find |v|. v = -2i + 3j - 3k
Find |v|. v = -i - j + k
Find |v|. v = i - j + k
Find |v|. v = -6i + 12j + 4k
Find |v|. v = 3i - 6j - 2k
The vector v has initial point P and terminal point Q. Write v in the form ai + bj + ck; that is, find its position vector.P = (-1, 4, -2); Q = (6, 2, 2)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj + ck; that is, find its position vector.P = (-2, -1, 4); Q = (6, -2, 4)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj + ck; that is, find its position vector.P = (-3, 2, 0); Q = (6, 5, -1)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj + ck; that is, find its position vector.P = (3, 2, -1); Q = (5, 6, 0)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj + ck; that is, find its position vector.P = (0, 0, 0); Q = (-3, -5, 4)
The vector v has initial point P and terminal point Q. Write v in the form ai + bj + ck; that is, find its position vector.P = (0, 0, 0); Q = (3, 4, -1)
Opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. (-2, -3, 0); (-6, 7, 1)
Opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. (-1, 0, 2); (4, 2, 5)
Opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. (5, 6, 1); (3, 8, 2)
Opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. (1, 2, 3); (3, 4, 5)
Opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. (0, 0, 0); (4, 2, 2)
Opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box. (0, 0, 0); (2, 1, 3)
Find the distance from to P2 to P2.P1 = (2, -3, -3) and P2 = (4, 1, -1)
Find the distance from to P2 to P2.P1 = (4, -2, -2) and P2 = (3, 2, 1)
Find the distance from to P2 to P2.P1 = (-2,2,3) and P2 = (4,0,-3)
Find the distance from to P2 to P2.P1 = (-1,2, -3) and P2 = (0,-2,1)
Find the distance from to P2 to P2.P1 = (0, 0, 0) and P2 = (1, -2, 3)
Find the distance from to P2 to P2.P1 = (0, 0, 0) and P2 = (4, 1, 2)
Describe the set of points defined by the equation(s). x = 3 and z = 1
Describe the set of points defined by the equation(s). .x = 1 and y = 2
Describe the set of points defined by the equation(s). z = -3
Describe the set of points defined by the equation(s). x = -4
Describe the set of points defined by the equation(s). y = 3
Describe the set of points defined by the equation(s). z = 2
Describe the set of points defined by the equation(s). x = 0
Describe the set of points defined by the equation(s). y = 0
True or False. A vector in space may be described by specifying its magnitude and its direction angles.
True or False. In space, the dot product of two vectors is a positive number.
The sum of the squares of the direction cosines of a vector in space add up to _______.
If v = ai + bj + ck is a vector in space, the scalars a, b, c are called the________ of v.
In space, points of the form lie in a plane called the ______.
The distance d from P1 = (x1, y) to P2 = (x2, y2) is d = _______.
Prove the polarization identity,|u + c|2 - |u – v|2 = 4(u.v)
In the definition of work given in this section, what is the work done if F is orthogonal to AB(vector)
Let v and w denote two nonzero vectors. Show that the vectors |w|v + |v|w and |w|v - |v|w are orthogonal.
Let v and w denote two nonzero vectors. Show that the vector v - αw is orthogonal to w if α = v•w/|w|2
(a) If u and v have the same magnitude, show that u + v and u - v are orthogonal. (b) Use this to prove that an angle inscribed in a semicircle is a right angle (see the figure). -V
Show that the projection of v onto i is (v.i). Then show that we can always write a vector v as v = (v.i)i + (v.j)j
Suppose that v and w are unit vectors. If the angle between v and i is and that between w and i is β used the idea of the dot product v. w to prove thatcos(α - β) = cosαcosβ + sinαsinβ
If v is a unit vector and the angle between v and i is α show that v = cosαi + sinαJ.
Prove property (5), 0•v = 0
Prove the distributive property: u • (v + w) = u • v + u • w
Find the acute angle that a constant unit force vector makes with the positive x-axis if the work done by the force in moving a particle from to equals 2.
A bulldozer exerts 1000 pounds of force to prevent a 5000-pound boulder from rolling down a hill. Determine the angle of inclination of the hill.
Billy and Timmy are using a ramp to load furniture into a truck. While rolling a 250-pound piano up the ramp, they discover that the truck is too full of other furniture for the piano to fit. Timmy holds the piano in place on the ramp while Billy repositions other items to make room for it in the
A Pontiac Bonneville with a gross weight of 4500 pounds is parked on a street with a 10° grade. Find the magnitude of the force required to keep the Bonneville from rolling down the hill. What is the magnitude of the force perpendicular to the hill?
A Toyota Sienna with a gross weight of 5300 pounds is parked on a street with a grade. See the figure. Find the magnitude of the force required to keep the Sienna from rolling down the hill. What is the magnitude of the force perpendicular to the hill? Weight = 5300 pounds %3D
Let the vector R represent the amount of rainfall, in inches, whose direction is the inclination of the rain to a rain gauge. Let the vector A represent the area, in square inches, whose direction is the orientation of the opening of the rain gauge. See the figure. The volume of rain collected in
The amount of energy collected by a solar panel depends on the intensity of the sun’s rays and the area of the panel. Let the vector I represent the intensity, in watts per square centimeter, having the direction of the sun’s rays. Let the vector A represent the area, in square centimeters,
A wagon is pulled horizontally by exerting a force of 20 pounds on the handle at an angle of 60° with the horizontal. How much work is done in moving the wagon 100 feet?
Find the work done by a force of 3 pounds acting in the direction 60° to the horizontal in moving an object 6 feet (0,0) to (6,0).
Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.v = i - 3j, w = 4i - j
Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.v = 3i + j, w = -2i - j
Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.v = 2i - j, w = i - 2j
Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.v = i - j, w = -i - 2j
Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w. v = -3i + 2j, w = 2i + j
Decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.v = 2i - 3j, w = i - j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. Find b so that the vectors v = i + j and w = i + bj are orthogonal.
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. Find a so that the vectors v = i - aj and w = 2i + 3j are orthogonal.
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = i, w = -3j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 4i, w = j
(a) Find the dot product.(b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 3i - 4j, w = 9i - 12j

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