 9.4.1: A ______ is a quantity that has both magnitude and direction
 9.4.2: If v is a vector, then v + 1 v2 =
 9.4.3: A vector u for which 7 u 7 = 1 is called a(n) ______ vector.
 9.4.4: If v = 6a, b7 is an algebraic vector whose initial point is the ori...
 9.4.5: If v = ai + bj, then a is called the _________ component of v and b...
 9.4.6: If F1 and F2 are two forces simultaneously acting on an object, the...
 9.4.7: True or False Force is an example of a vector.
 9.4.8: True or False Mass is an example of a vector.
 9.4.9: In 916, use the vectors in the figure at the right to graph each of...
 9.4.10: In 916, use the vectors in the figure at the right to graph each of...
 9.4.11: In 916, use the vectors in the figure at the right to graph each of...
 9.4.12: In 916, use the vectors in the figure at the right to graph each of...
 9.4.13: In 916, use the vectors in the figure at the right to graph each of...
 9.4.14: In 916, use the vectors in the figure at the right to graph each of...
 9.4.15: In 916, use the vectors in the figure at the right to graph each of...
 9.4.16: In 916, use the vectors in the figure at the right to graph each of...
 9.4.17: In 1724, use the figure at the right. Determine whether the given s...
 9.4.18: In 1724, use the figure at the right. Determine whether the given s...
 9.4.19: In 1724, use the figure at the right. Determine whether the given s...
 9.4.20: In 1724, use the figure at the right. Determine whether the given s...
 9.4.21: In 1724, use the figure at the right. Determine whether the given s...
 9.4.22: In 1724, use the figure at the right. Determine whether the given s...
 9.4.23: In 1724, use the figure at the right. Determine whether the given s...
 9.4.24: In 1724, use the figure at the right. Determine whether the given s...
 9.4.25: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.26: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.27: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.28: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.29: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.30: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.31: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.32: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.33: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.34: In 2734, the vector v has initial point P and terminal point Q. Wri...
 9.4.35: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.36: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.37: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.38: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.39: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.40: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.41: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.42: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.43: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.44: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.45: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.46: In 4146, find each quantity if v = 3i  5j and w = 2i + 3j.
 9.4.47: In 4752, find the unit vector in the same direction as v.
 9.4.48: In 4752, find the unit vector in the same direction as v.
 9.4.49: In 4752, find the unit vector in the same direction as v.
 9.4.50: In 4752, find the unit vector in the same direction as v.
 9.4.51: In 4752, find the unit vector in the same direction as v.
 9.4.52: In 4752, find the unit vector in the same direction as v.
 9.4.53: Find a vector v whose magnitude is 4 and whose component in the i d...
 9.4.54: Find a vector v whose magnitude is 3 and whose component in the i d...
 9.4.55: If v = 2i  j and w = xi + 3j, find all numbers x for which 7 v + w...
 9.4.56: If P = 1 3, 12 and Q = 1x, 42, find all numbers x such that the ve...
 9.4.57: In 5762, write the vector v in the form ai + bj, given its magnitud...
 9.4.58: In 5762, write the vector v in the form ai + bj, given its magnitud...
 9.4.59: In 5762, write the vector v in the form ai + bj, given its magnitud...
 9.4.60: In 5762, write the vector v in the form ai + bj, given its magnitud...
 9.4.61: In 5762, write the vector v in the form ai + bj, given its magnitud...
 9.4.62: In 5762, write the vector v in the form ai + bj, given its magnitud...
 9.4.63: In 6370, find the direction angle of v for each vector.
 9.4.64: In 6370, find the direction angle of v for each vector.
 9.4.65: In 6370, find the direction angle of v for each vector.
 9.4.66: In 6370, find the direction angle of v for each vector.
 9.4.67: In 6370, find the direction angle of v for each vector.
 9.4.68: In 6370, find the direction angle of v for each vector.
 9.4.69: In 6370, find the direction angle of v for each vector.
 9.4.70: In 6370, find the direction angle of v for each vector.
 9.4.71: The field of computer graphics utilizes vectors to compute translat...
 9.4.72: Refer to 71. The points 1 3, 02, 1 1, 22, 13, 12, and 11, 32 are...
 9.4.73: A child pulls a wagon with a force of 40 pounds. The handle of the ...
 9.4.74: A man pushes a wheelbarrow up an incline of 20 with a force of 100 ...
 9.4.75: Two forces of magnitude 40 newtons (N) and 60 N act on an object at...
 9.4.76: Two forces of magnitude 30 newtons (N) and 70 N act on an object at...
 9.4.77: A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles p...
 9.4.78: An Airbus A320 jet maintains a constant airspeed of 500 mi/hr heade...
 9.4.79: An airplane has an airspeed of 500 kilometers per hour (km/hr) bear...
 9.4.80: An airplane has an airspeed of 600 km/hr bearing S30E. The wind vel...
 9.4.81: A magnitude of 700 pounds of force is required to hold a boat and i...
 9.4.82: A magnitude of 1200 pounds of force is required to prevent a car fr...
 9.4.83: Vectors 605 should a motorboat capable of maintaining a constant sp...
 9.4.84: The pilot of an aircraft wishes to head directly east but is faced ...
 9.4.85: A weight of 1000 pounds is suspended from two cables as shown in th...
 9.4.86: A weight of 800 pounds is suspended from two cables, as shown in th...
 9.4.87: A tightrope walker located at a certain point deflects the rope as ...
 9.4.88: Repeat if the angle on the left is 3.8, the angle on the right is 2...
 9.4.89: At a county fair truck pull, two pickup trucks are attached to the ...
 9.4.90: A farmer wishes to remove a stump from a field by pulling it out wi...
 9.4.91: Show on the following graph the force needed for the object at P to...
 9.4.92: Open the Vectors applet. Draw the directed line segment from P1 = 1...
 9.4.93: Open the Vectors applet. Suppose v = 2i + 3j and w = 4i  3j. (a) D...
 9.4.94: Explain in your own words what a vector is. Give an example of a ve...
 9.4.95: Write a brief paragraph comparing the algebra of complex numbers an...
 9.4.96: Explain the difference between an algebraic vector and a position v...
Solutions for Chapter 9.4: Vectors
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 9.4: Vectors
Get Full SolutionsSince 96 problems in chapter 9.4: Vectors have been answered, more than 56104 students have viewed full stepbystep solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. Chapter 9.4: Vectors includes 96 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.