 6.4.1: Fill in the blanks The ________ ________ of two vectors yields a sc...
 6.4.2: Fill in the blanks If is the angle between two nonzero vectors and ...
 6.4.3: Fill in the blanks The vectors and are ________ if
 6.4.4: Fill in the blanks The projection of onto is given by
 6.4.5: Fill in the blanks The work done by a constant force as its point o...
 6.4.6: In Exercises 18, find the dot product of and v
 6.4.7: In Exercises 18, find the dot product of and v
 6.4.8: In Exercises 18, find the dot product of and v
 6.4.9: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.10: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.11: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.12: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.13: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.14: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.15: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.16: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.17: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.18: In Exercises 918, use the vectors and to find the indicated quantit...
 6.4.19: In Exercises 1924, use the dot product to find the magnitude of u.
 6.4.20: In Exercises 1924, use the dot product to find the magnitude of u.
 6.4.21: In Exercises 1924, use the dot product to find the magnitude of u.
 6.4.22: In Exercises 1924, use the dot product to find the magnitude of u.
 6.4.23: In Exercises 1924, use the dot product to find the magnitude of u.
 6.4.24: In Exercises 1924, use the dot product to find the magnitude of u.
 6.4.25: In Exercises 2534, find the angle between the vectors
 6.4.26: In Exercises 2534, find the angle between the vectors
 6.4.27: In Exercises 2534, find the angle between the vectors
 6.4.28: In Exercises 2534, find the angle between the vectors
 6.4.29: In Exercises 2534, find the angle between the vectors
 6.4.30: In Exercises 2534, find the angle between the vectors
 6.4.31: In Exercises 2534, find the angle between the vectors
 6.4.32: In Exercises 2534, find the angle between the vectors
 6.4.33: In Exercises 2534, find the angle between the vectors
 6.4.34: In Exercises 2534, find the angle between the vectors
 6.4.35: In Exercises 3538, graph the vectors and find the degree measure of...
 6.4.36: In Exercises 3538, graph the vectors and find the degree measure of...
 6.4.37: In Exercises 3538, graph the vectors and find the degree measure of...
 6.4.38: In Exercises 3538, graph the vectors and find the degree measure of...
 6.4.39: In Exercises 3942, use vectors to find the interior angles of the t...
 6.4.40: In Exercises 3942, use vectors to find the interior angles of the t...
 6.4.41: In Exercises 3942, use vectors to find the interior angles of the t...
 6.4.42: In Exercises 3942, use vectors to find the interior angles of the t...
 6.4.43: In Exercises 4346, find where is the angle between and v
 6.4.44: In Exercises 4346, find where is the angle between and v
 6.4.45: In Exercises 4346, find where is the angle between and v
 6.4.46: In Exercises 4346, find where is the angle between and v_u_ _ 4, _v...
 6.4.47: In Exercises 4752, determine whether and are orthogonal, parallel, ...
 6.4.48: In Exercises 4752, determine whether and are orthogonal, parallel, ...
 6.4.49: In Exercises 4752, determine whether and are orthogonal, parallel, ...
 6.4.50: In Exercises 4752, determine whether and are orthogonal, parallel, ...
 6.4.51: In Exercises 4752, determine whether and are orthogonal, parallel, ...
 6.4.52: In Exercises 4752, determine whether and are orthogonal, parallel, ...
 6.4.53: In Exercises 5356, find the projection of onto . Then write as the ...
 6.4.54: In Exercises 5356, find the projection of onto . Then write as the ...
 6.4.55: In Exercises 5356, find the projection of onto . Then write as the ...
 6.4.56: In Exercises 5356, find the projection of onto . Then write as the ...
 6.4.57: In Exercises 57 and 58, use the graph to determine mentally the pro...
 6.4.58: In Exercises 57 and 58, use the graph to determine mentally the pro...
 6.4.59: In Exercises 5962, find two vectors in opposite directions that are...
 6.4.60: In Exercises 5962, find two vectors in opposite directions that are...
 6.4.61: In Exercises 5962, find two vectors in opposite directions that are...
 6.4.62: In Exercises 5962, find two vectors in opposite directions that are...
 6.4.63: In Exercises 63 and 64, find the work done in moving a particle fro...
 6.4.64: In Exercises 63 and 64, find the work done in moving a particle fro...
 6.4.65: Revenue The vector gives the numbers of units of two types of bakin...
 6.4.66: Revenue The vector gives the numbers of hamburgers and hot dogs, re...
 6.4.67: Braking Load A truck with a gross weight of 30,000 pounds is parked...
 6.4.68: Braking Load A sport utility vehicle with a gross weight of 5400 po...
 6.4.69: Work Determine the work done by a person lifting a 25kilogram (245...
 6.4.70: Work Determine the work done by a crane lifting a 2400pound car 5 ...
 6.4.71: Work A force of 45 pounds exerted at an angle of above the horizont...
 6.4.72: Work A tractor pulls a log 800 meters, and the tension in the cable...
 6.4.73: Work One of the events in a local strongman contest is to pull a ce...
 6.4.74: Work A toy wagon is pulled by exerting a force of 25 pounds on a ha...
 6.4.75: The work done by a constant force acting along the line of motion o...
 6.4.76: A sliding door moves along the line of vector If a force is applied...
 6.4.77: Think About It What is known about , the angle between two nonzero ...
 6.4.78: Think About It What can be said about the vectors and under each co...
 6.4.79: Proof Use vectors to prove that the diagonals of a rhombus are perp...
 6.4.80: Proof Prove the following.
 6.4.81: In Exercises 8184, perform the operation and write the result in st...
 6.4.82: In Exercises 8184, perform the operation and write the result in st...
 6.4.83: In Exercises 8184, perform the operation and write the result in st...
 6.4.84: In Exercises 8184, perform the operation and write the result in st...
 6.4.85: In Exercises 8588, find all solutions of the equation in the interval
 6.4.86: In Exercises 8588, find all solutions of the equation in the interval
 6.4.87: In Exercises 8588, find all solutions of the equation in the interval
 6.4.88: In Exercises 8588, find all solutions of the equation in the interval
 6.4.89: In Exercises 8992, find the exact value of the trigonometric functi...
 6.4.90: In Exercises 8992, find the exact value of the trigonometric functi...
 6.4.91: In Exercises 8992, find the exact value of the trigonometric functi...
 6.4.92: In Exercises 8992, find the exact value of the trigonometric functi...
Solutions for Chapter 6.4: Vectors and Dot Products
Full solutions for Precalculus  7th Edition
ISBN: 9780618643448
Solutions for Chapter 6.4: Vectors and Dot Products
Get Full SolutionsChapter 6.4: Vectors and Dot Products includes 92 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus, edition: 7. Since 92 problems in chapter 6.4: Vectors and Dot Products have been answered, more than 24372 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus was written by and is associated to the ISBN: 9780618643448.

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

Augmented matrix
A matrix that represents a system of equations.

Cycloid
The graph of the parametric equations

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

First quartile
See Quartile.

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Obtuse triangle
A triangle in which one angle is greater than 90°.

Oddeven identity
For a basic trigonometric function f, an identity relating f(x) to f(x).

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Reciprocal of a real number
See Multiplicative inverse of a real number.

Reflection
Two points that are symmetric with respect to a lineor a point.

Sine
The function y = sin x.

Slope
Ratio change in y/change in x

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Weighted mean
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.

Weights
See Weighted mean.