 1.4.1: Evaluate the determinants in Exercises 14.2 4 1 3
 1.4.2: Evaluate the determinants in Exercises 14.0 5 1 6
 1.4.3: Evaluate the determinants in Exercises 14.135 027 103
 1.4.4: Evaluate the determinants in Exercises 14.2 0 1 2 3 6 1 4 8 2
 1.4.5: In Exercises 57, calculate the indicated cross products, using both...
 1.4.6: In Exercises 57, calculate the indicated cross products, using both...
 1.4.7: In Exercises 57, calculate the indicated cross products, using both...
 1.4.8: Prove property 3 of cross products, using properties 1 and 2.
 1.4.9: If a b = 3i 7j 2k, what is (a + b) (a b)?
 1.4.10: Calculate the area of the parallelogram having vertices (1, 1), (3,...
 1.4.11: Calculate the area of the parallelogram having vertices (1, 2, 3), ...
 1.4.12: Find a unit vector that is perpendicular to both 2i + j 3k and i + k.
 1.4.13: If (a b) c = 0, what can you say about the geometric relation betwe...
 1.4.14: Compute the area of the triangles described in Exercises 1417.The t...
 1.4.15: Compute the area of the triangles described in Exercises 1417.The t...
 1.4.16: Compute the area of the triangles described in Exercises 1417.The t...
 1.4.17: Compute the area of the triangles described in Exercises 1417.The t...
 1.4.18: Find the volume of the parallelepiped determined by a = 3i j, b = 2...
 1.4.19: What is the volume of the parallelepiped with vertices (3, 0, 1), (...
 1.4.20: Verify that (a b) c = a1 a2 a3 b1 b2 b3 c1 c2 c3
 1.4.21: Show that (a b) c = a (b c) using Exercise 20.
 1.4.22: Use geometry to show that (a b) c = b (a c).
 1.4.23: (a) Show that the area of the triangle with vertices P1(x1, y1), P2...
 1.4.24: Suppose that a, b, and c are noncoplanar vectors in R3, so that the...
 1.4.25: Suppose that you are given nonzero vectors a, b, and c in R3. Use d...
 1.4.26: Suppose a, b, c, and d are vectors in R3. Indicate which of the fol...
 1.4.27: Exercises 2732 concern several identities for vectors a, b, c, and ...
 1.4.28: Exercises 2732 concern several identities for vectors a, b, c, and ...
 1.4.29: Exercises 2732 concern several identities for vectors a, b, c, and ...
 1.4.30: Exercises 2732 concern several identities for vectors a, b, c, and ...
 1.4.31: Exercises 2732 concern several identities for vectors a, b, c, and ...
 1.4.32: Exercises 2732 concern several identities for vectors a, b, c, and ...
 1.4.33: Establish the identity (a b)(c d) = (a c)(b d) (a d)(b c) of Exerci...
 1.4.34: Egbert applies a 20 lb force at the edge of a 4 ft wide door that i...
 1.4.35: Gertrude is changing a flat tire with a tire iron. The tire iron is...
 1.4.36: Egbert is trying to open a jar of grape jelly. The radius of the li...
 1.4.37: A 50 lb child is sitting on one end of a seesaw, 3 ft from the cent...
 1.4.38: For this problem, note that the radius of the earth is approximatel...
 1.4.39: Archie, the cockroach, and Annie, the ant, are on an LP record. Arc...
 1.4.40: A top is spinning with a constant angular speed of 12 radians/sec. ...
 1.4.41: There is a difficulty involved with our definition of the angular v...
Solutions for Chapter 1.4: The Cross Product
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 1.4: The Cross Product
Get Full SolutionsSince 41 problems in chapter 1.4: The Cross Product have been answered, more than 12496 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Chapter 1.4: The Cross Product includes 41 full stepbystep solutions.

Circle graph
A circular graphical display of categorical data

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Directed distance
See Polar coordinates.

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Extracting square roots
A method for solving equations in the form x 2 = k.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Order of an m x n matrix
The order of an m x n matrix is m x n.

Parallel lines
Two lines that are both vertical or have equal slopes.

Polar axis
See Polar coordinate system.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Right triangle
A triangle with a 90° angle.

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Variable
A letter that represents an unspecified number.

Variance
The square of the standard deviation.