- 11.4.1E: In Exercises 1–8, find the length and direction (when defined) of u...
- 11.4.2E: u = 2i + 3j, v = -i + j
- 11.4.3E: u = 2i - 2j + 4k, v = -i + j - 2k
- 11.4.4E: u = i + j - k, v = 0
- 11.4.5E: u = 2i, v = -3j
- 11.4.6E: u = i x j, v = j x k
- 11.4.7E: u = -8i - 2j - 4k, v = 2i + 2j + k
- 11.4.8E: u = 3/2i – 1/2j + k, v = i + j + 2k
- 11.4.9E: In Exercises 9–14, sketch the coordinate axes and then include the ...
- 11.4.10E: u = i - k, v = j
- 11.4.11E: u = i - k, v = j + k
- 11.4.12E: u = 2i - j, v = i + 2j
- 11.4.13E: u = i + j, v = i - j
- 11.4.14E: u = j + 2k, v = i
- 11.4.15E: In Exercises 15–18,a. Find the area of the triangle determined by t...
- 11.4.16E: P(1, 1, 1), Q(2, 1, 3), R(3, -1, 1)
- 11.4.17E: P(2, -2, 1), Q(3, -1, 2), R(3, -1, 1)
- 11.4.18E: P( -2, 2, 0), Q(0, 1, -1), R( -1, 2, -2)
- 11.4.19E: In Exercises 19–22, verify that ( u x v). w = (v x w).u = (w x u )....
- 11.4.20E: i - j + k 2i + j - 2k -i + 2j - k
- 11.4.21E: 2i + j 2i - j + k i + 2k
- 11.4.22E: i+ j - 2k -i - k 2i + 4j - 2k
- 11.4.23E: Parallel and perpendicular vectors Let .Which vectors, if any, are ...
- 11.4.24E: Parallel and perpendicular vectors Let u = i + 2j - k, v = -i + j +...
- 11.4.25E: In Exercises 25 and 26, find the magnitude of the torque exerted by...
- 11.4.27E: Which of the following are always true, and which are not always tr...
- 11.4.28E: Which of the following are always true, and which are not always tr...
- 11.4.29E: Given nonzero vectors u, v, and w, use dot product and cross produc...
- 11.4.30E: Compute (i X j) X j and i X (j X j).What can you conclude about the...
- 11.4.31E: Let u, v, and w be vectors. Which of the following make sense, and ...
- 11.4.32E: Cross products of three vectors Show that except in degenerate case...
- 11.4.33E: Cancellation in cross products If u X v = u X w and then does v = w...
- 11.4.34E: Double cancellation If and if and u.v = u.w, then does v = w?Give r...
- 11.4.35E: Find the areas of the parallelograms whose vertices are given in Ex...
- 11.4.36E: A(0, 0), B(7, 3), C(9, 8), D(2, 5)
- 11.4.37E: A(-1, 2), B(2, 0), C(7, 1), D(4, 3)
- 11.4.38E: A(-6, 0), B(1, -4), C(3, 1), D (-4, 5)
- 11.4.40E: A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), D(0, 3, 2)
- 11.4.39E: A(0, 0, 0), B(3, 2, 4), C(5, 1, 4), D(2, -1, 0)
- 11.4.41E: Find the areas of the triangles whose vertices are given in Exercis...
- 11.4.43E: A(-5, 3), B(1, -2), C(6, -2)
- 11.4.44E: A(-6, 0), B(10, -5), C(-2, 4)
- 11.4.45E: A(1, 0, 0), B(0, 2, 0), C(0, 0, -1)
- 11.4.46E: A(0, 0, 0), B(-1, 1, -1), C(3, 0, 3)
- 11.4.47E: A(1, -1, 1), B(0, 1, 1), C(1, 0, -1)
- 11.4.48E: Find the volume of a parallelepiped if four of its eight vertices a...
- 11.4.49E: Triangle area Find a 2 X 2 determinant formula for the area of the ...
- 11.4.50E: Triangle area Find a concise 3 X 3 determinant formula that gives t...
Solutions for Chapter 11.4: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals | 2nd Edition
Additive identity for the complex numbers
0 + 0i is the complex number zero
Axis of symmetry
See Line of symmetry.
Trigonometric functions when applied to real numbers are circular functions
A method of solving a system of linear equations
Arrows that have the same magnitude and direction.
An equation that is always true throughout its domain.
The notation dy/dx for the derivative of ƒ.
Line of symmetry
A line over which a graph is the mirror image of itself
Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial
A polynomial with exactly one term.
Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.
Product of complex numbers
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
See Reference triangle
Reflexive property of equality
a = a
If a polynomial f(x) is divided by x - c , the remainder is ƒ(c)
Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.
a - b = a + (-b)
See Conversion factor.
Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.
The x-value of the left side of the viewing window,.