 11.3.1: 3, 1, 2 6, 0, 5 =
 11.3.2: Suppose that u, v, and w are vectors in 3space such thatu = 5, u v...
 11.3.3: For the vectors u and v in the preceding exercise, if the anglebetw...
 11.3.4: The direction cosines of 2, 1, 3 are cos = ,cos = , and cos =
 11.3.5: The orthogonal projection of v = 10i on b = 3i + j is.
 11.3.6: The accompanying figure shows six vectors that areequally spaced ar...
 11.3.7: (a) Use vectors to show that A(2, 1, 1), B(3, 2, 1),and C(7, 0, 2) ...
 11.3.8: (a) Show that if v = ai + bj is a vector in 2space, thenthe vector...
 11.3.9: Explain why each of the following expressions makesno sense.(a) u (...
 11.3.10: Explain why each of the following expressions makessense.(a) (u v)w...
 11.3.11: Verify parts (b) and (c) of Theorem 11.3.2 for the vectorsu = 6i j ...
 11.3.12: Let u = 1, 2, v = 4, 2, and w = 6, 0. Find(a) u (7v + w) (b) (u w)w...
 11.3.13: Find r so that the vector from the point A(1, 1, 3) to thepoint B(3...
 11.3.14: Find two unit vectors in 2space that make an angle of 45with 4i + 3j.
 11.3.15: 1516 Find the direction cosines of v and confirm that they satisfyE...
 11.3.16: 1516 Find the direction cosines of v and confirm that they satisfyE...
 11.3.17: Show that the direction cosines of a vector satisfycos2 + cos2 + co...
 11.3.18: Let and be the angles shown in the accompanyingfigure. Show that th...
 11.3.19: The accompanying figure shows a cube.(a) Find the angle between the...
 11.3.20: Show that two nonzero vectors v1 and v2 are orthogonalif and only i...
 11.3.21: Use the result in Exercise 18 to find the direction angles ofthe ve...
 11.3.22: Find, to the nearest degree, the acute angle formed by twodiagonals...
 11.3.23: Find, to the nearest degree, the angles that a diagonal of abox wit...
 11.3.24: In each part, find the vector component of v along b andthe vector ...
 11.3.25: In each part, find the vector component of v along b and thevector ...
 11.3.26: 2627 Express the vector v as the sum of a vector parallel to band a...
 11.3.27: 2627 Express the vector v as the sum of a vector parallel to band a...
 11.3.28: 2831 TrueFalse Determine whether the statement is true orfalse. Exp...
 11.3.29: 2831 TrueFalse Determine whether the statement is true orfalse. Exp...
 11.3.30: 2831 TrueFalse Determine whether the statement is true orfalse. Exp...
 11.3.31: 2831 TrueFalse Determine whether the statement is true orfalse. Exp...
 11.3.32: If L is a line in 2space or 3space that passes through thepoints ...
 11.3.33: Use the method of Exercise 32 to find the distance fromthe point P ...
 11.3.34: As shown in the accompanying figure, a child with mass34 kg is seat...
 11.3.35: For the child in Exercise 34, estimate how much force mustbe applie...
 11.3.36: Suppose that the slide in Exercise 34 is 4 m long. Estimatethe work...
 11.3.37: A box is dragged along the floor by a rope that applies aforce of 5...
 11.3.38: Find the work done by a force F = 3j pounds applied toa point that ...
 11.3.39: A force of F = 4i 6j + k newtons is applied to a pointthat moves a ...
 11.3.40: A boat travels 100 meters due north while the wind exertsa force of...
 11.3.41: Let u and v be adjacent sides of a parallelogram. Usevectors to pro...
 11.3.42: Let u and v be adjacent sides of a parallelogram. Usevectors to pro...
 11.3.43: Prove thatu + v2 + u v2 = 2u2 + 2v2and interpret the result geometr...
 11.3.44: Prove: u v = 14 u + v2 14 u v2.
 11.3.45: Show that if v1, v2, and v3 are mutually orthogonal nonzerovectors ...
 11.3.46: Show that the three vectorsv1 = 3i j + 2k, v2 = i + j k, v3 = i 5j ...
 11.3.47: For each x in (, +), let u(x) be the vector from theorigin to the p...
 11.3.48: Let u be a unit vector in the xyplane of an xyzcoordinatesystem, ...
 11.3.49: Prove parts (b) and (e) of Theorem 11.3.2 for vectors in3space.
 11.3.50: Writing Discuss some of the similarities and differencesbetween the...
 11.3.51: Writing Discuss the merits of the following claim: Supposean algebr...
Solutions for Chapter 11.3: DOT PRODUCT; PROJECTIONS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 11.3: DOT PRODUCT; PROJECTIONS
Get Full SolutionsSince 51 problems in chapter 11.3: DOT PRODUCT; PROJECTIONS have been answered, more than 38221 students have viewed full stepbystep solutions from this chapter. Chapter 11.3: DOT PRODUCT; PROJECTIONS includes 51 full stepbystep solutions. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Dependent variable
Variable representing the range value of a function (usually y)

Determinant
A number that is associated with a square matrix

Equal matrices
Matrices that have the same order and equal corresponding elements.

Exponential regression
A procedure for fitting an exponential function to a set of data.

Imaginary axis
See Complex plane.

Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Inverse secant function
The function y = sec1 x

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Symmetric difference quotient of ƒ at a
ƒ(x + h)  ƒ(x  h) 2h

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.