 12.2.1: Are the following quantities vectors or scalars? Explain. (a) The c...
 12.2.2: What is the relationship between the point (4, 7) and the vector ? ...
 12.2.3: Name all the equal vectors in the parallelogram shown.
 12.2.4: Write each combination of vectors as a single vector.
 12.2.5: Copy the vectors in the figure and use them to draw the following v...
 12.2.6: Copy the vectors in the figure and use them to draw the following v...
 12.2.7: In the figure, the tip of and the tail of are both the midpoint of ...
 12.2.8: If the vectors in the figure satisfy and , what is ?
 12.2.9: Find a vector with representation given by the directed line segmen...
 12.2.10: Find a vector with representation given by the directed line segmen...
 12.2.11: Find a vector with representation given by the directed line segmen...
 12.2.12: Find a vector with representation given by the directed line segmen...
 12.2.13: Find a vector with representation given by the directed line segmen...
 12.2.14: Find a vector with representation given by the directed line segmen...
 12.2.15: Find the sum of the given vectors and illustrate geometrically.
 12.2.16: Find the sum of the given vectors and illustrate geometrically.
 12.2.17: Find the sum of the given vectors and illustrate geometrically.
 12.2.18: Find the sum of the given vectors and illustrate geometrically.
 12.2.19: Find a b, 2a 3b, , and .
 12.2.20: Find a b, 2a 3b, , and .
 12.2.21: Find a b, 2a 3b, , and .
 12.2.22: Find a b, 2a 3b, , and .
 12.2.23: Find a unit vector that has the same direction as the given vector.
 12.2.24: Find a unit vector that has the same direction as the given vector.
 12.2.25: Find a unit vector that has the same direction as the given vector.
 12.2.26: Find a vector that has the same direction as but has length 6.
 12.2.27: What is the angle between the given vector and the positive directi...
 12.2.28: What is the angle between the given vector and the positive directi...
 12.2.29: If lies in the first quadrant and makes an angle with the positive ...
 12.2.30: If a child pulls a sled through the snow on a level path with a for...
 12.2.31: A quarterback throws a football with angle of elevation and speed ....
 12.2.32: Find the magnitude of the resultant force and the angle it makes wi...
 12.2.33: Find the magnitude of the resultant force and the angle it makes wi...
 12.2.34: The magnitude of a velocity vector is called speed. Suppose that a ...
 12.2.35: A woman walks due west on the deck of a ship at 3 mi_h. The ship is...
 12.2.36: Ropes 3 m and 5 m in length are fastened to a holiday decoration th...
 12.2.37: A clothesline is tied between two poles, 8 m apart. The line is qui...
 12.2.38: The tension T at each end of the chain has magnitude 25 N (see the ...
 12.2.39: A boatman wants to cross a canal that is 3 km wide and wants to lan...
 12.2.40: Three forces act on an object. Two of the forces are at an angle of...
 12.2.41: Find the unit vectors that are parallel to the tangent line to the ...
 12.2.42: (a) Find the unit vectors that are parallel to the tangent line to ...
 12.2.43: If , , and are the vertices of a triangle, find
 12.2.44: Let be the point on the line segment that is twice as far from as i...
 12.2.45: (a) Draw the vectors , , and (b) Show, by means of a sketch, that t...
 12.2.46: Suppose that and are nonzero vectors that are not parallel and is a...
 12.2.47: If and , describe the set of all points such that .
 12.2.48: If , , and , describe the set of all points such that , where .
 12.2.49: Figure 16 gives a geometric demonstration of Property 2 of vectors....
 12.2.50: Prove Property 5 of vectors algebraically for the case . Then use s...
 12.2.51: Use vectors to prove that the line joining the midpoints of two sid...
 12.2.52: Suppose the three coordinate planes are all mirrored and a light ra...
Solutions for Chapter 12.2: VECTORS
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 12.2: VECTORS
Get Full SolutionsMultivariable Calculus, was written by and is associated to the ISBN: 9780538497879. Chapter 12.2: VECTORS includes 52 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Since 52 problems in chapter 12.2: VECTORS have been answered, more than 22520 students have viewed full stepbystep solutions from this chapter.

Acceleration due to gravity
g ? 32 ft/sec2 ? 9.8 m/sec

Acute triangle
A triangle in which all angles measure less than 90°

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Compounded continuously
Interest compounded using the formula A = Pert

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Inverse cotangent function
The function y = cot1 x

Matrix element
Any of the real numbers in a matrix

Measure of spread
A measure that tells how widely distributed data are.

Multiplicative identity for matrices
See Identity matrix

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Range screen
See Viewing window.

Scalar
A real number.

Second quartile
See Quartile.

Semimajor axis
The distance from the center to a vertex of an ellipse.

Unbounded interval
An interval that extends to ? or ? (or both).

zaxis
Usually the third dimension in Cartesian space.