Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-3, let P(x, y) and Q(2, -3) be points in the xy-plane. Compute the distance between P and Q.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-3, let P(x, y) and Q(2, -3) be points in the xy-plane. Find the midpoint of the line segment PQ.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-3, let P(x, y) and Q(2, -3) be points in the xy-plane. If P is 5 units from Q, describe the position of P.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 46, let \(\mathbf{v}=\left\langle-4,\ 5\right\rangle=-4\mathbf{i}+5\mathbf{j}\) be a vector in the xy-plane. Find the magnitude of v.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 46, let \(\mathbf{v}=\left\langle-4,\ 5\right\rangle=-4\mathbf{i}+5\mathbf{j}\) be a vector in the xy-plane. Find a unit vector in the direction of v.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 46, let \(\mathbf{v}=\left\langle-4,\ 5\right\rangle=-4\mathbf{i}+5\mathbf{j}\) be a vector in the xy-plane. Find a vector 7 units long in the direction of -v.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Give a geometric description of the graph of \((x+1)^{2}+(y-5)^{2}=25\) in the xy-plane.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Give a geometric description of the graph of \(x=2-t,\ y=-4+2t\) in the xy-plane.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find the center and radius of the circle \(x^{2}+y^{2}+2 x-6 y+6=0\) in the xy-plane.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find a vector from P(2, 5) to Q(-1, -4) in the xy-plane.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, draw a sketch that shows the point. (3, 4, 2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, draw a sketch that shows the point. (2, -3, 6)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, draw a sketch that shows the point. (1, -2, -4)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 14, draw a sketch that shows the point. (-2, 3, -5)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, compute the distance between the points. (-1, 2, 5), (3, -4, 6)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, compute the distance between the points. (2, -1, -8), (6, -3, 4)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, compute the distance between the points. (a, b, c), (1, -3, 2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, compute the distance between the points. (x, y, z), (p, q, r)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, find the midpoint of the segment PQ. P(-1, 2, 5), Q(3, -4, 6)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, find the midpoint of the segment PQ. P(2, -1, -8), Q(6, -3, 4)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, find the midpoint of the segment PQ. P(2x, 2y, 2z), Q(-2, 8, 6)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 912, find the midpoint of the segment PQ. P(-a, -b, -c), Q(3a, 3b, 3c)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, write an equation for the sphere with the given point as its center and the given number as its radius. (5, -1, -2), 8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, write an equation for the sphere with the given point as its center and the given number as its radius. \((-1,\ 5,\ 8),\ \sqrt{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, write an equation for the sphere with the given point as its center and the given number as its radius. \((1,\ -3,\ 2),\ \sqrt{a},\ a>0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, write an equation for the sphere with the given point as its center and the given number as its radius. (p, q, r), 6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1722, sketch a graph of the equation. Label all intercepts. x + y + 3z = 9

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1722, sketch a graph of the equation. Label all intercepts. x + y - 2z = 8

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1722, sketch a graph of the equation. Label all intercepts. x + z = 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1722, sketch a graph of the equation. Label all intercepts. 2y + z = 6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1722, sketch a graph of the equation. Label all intercepts. x - 3y = 6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1722, sketch a graph of the equation. Label all intercepts. x = 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). r + v

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). r - w

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). \(\mathbf{v} \cdot \mathbf{w}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). |w|

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). \(\mathbf{r} \cdot(\mathbf{v}+\mathbf{w})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). \((\mathbf{r} \cdot \mathbf{v})+(\mathbf{r} \cdot \mathbf{w})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). w/|w|

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). \(\mathbf{i} \cdot \mathbf{r}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). \(\langle\mathbf{i} \cdot \mathbf{v}, \mathbf{j} \cdot \mathbf{v}, \mathbf{k} \cdot \mathbf{v}\rangle\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2332, evaluate the expression using \(\mathbf{r}=\langle 1,0,-3\rangle\), \(\mathbf{v}=\langle-3,4,-5\rangle\), and \(\mathbf{w}=\langle 4,-3,12\rangle\). \((\mathbf{r} \cdot \mathbf {v})\mathbf {w}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 33 and 34, let i point east, j point north, and k point up. Three-Dimensional Velocity An airplane just after takeoff is headed west and is climbing at a \(20^{\circ}\) angle relative to flat ground with an airspeed of 200 mph. If the wind is out of the northeast at 10 mph, calculate

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 33 and 34, let i point east, j point north, and k point up. Three-Dimensional Velocity A rocket soon after takeoff is headed east and is climbing at an \(80^{\circ}\) angle relative to flat ground with an airspeed of 12,000 mph. If the wind is out of the southwest at 8 mph, calculate

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, write the vector and parametric forms of the line through the point \(P_0\) in the direction of v. \(P_{0}(2,-1,5), \mathbf{v}=\langle 3,2,-7\rangle\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, write the vector and parametric forms of the line through the point \(P_0\) in the direction of v. \(P_{0}(-3,8,-1), \mathbf{v}=\langle -3,5,2\rangle\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, write the vector and parametric forms of the line through the point \(P_0\) in the direction of v. \(P_{0}(6,-9,0), \mathbf{v}=\langle 1,0,-4\rangle\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, write the vector and parametric forms of the line through the point \(P_0\) in the direction of v. \(P_{0}(0,-1,4), \mathbf{v}=\langle 0,0,1\rangle\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Find the distance from A to the midpoint of BC.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Find the vector from A to the midpoint of BC.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Write a vector equation of the line through A and B.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Write a vector equation of the line through A and the midpoint of BC.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Write parametric equations of the line through A and C.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Write parametric equations of the line through B and C.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Write parametric equations of the line through B and the midpoint of AC.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Write parametric equations of the line through C and the midpoint of AB.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). Is \(\triangle A B C\) equilateral, isosceles, or scalene?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3948, use the points A(-1, 2, 4), B(0, 6, -3), and C(2, -4, 1). If M is the midpoint of BC, what is the midpoint of AM?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, (a) sketch the line defined by the pair of equations, and (b) Writing to Learn give a geometric description of the line, including its direction and its position relative to the coordinate frame. x = 0, y = 0

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, (a) sketch the line defined by the pair of equations, and (b) Writing to Learn give a geometric description of the line, including its direction and its position relative to the coordinate frame. x = 0, z = 2

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, (a) sketch the line defined by the pair of equations, and (b) Writing to Learn give a geometric description of the line, including its direction and its position relative to the coordinate frame. x = -3, y = 0

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, (a) sketch the line defined by the pair of equations, and (b) Writing to Learn give a geometric description of the line, including its direction and its position relative to the coordinate frame. y = 1, z = 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Write a vector equation for the line through the distinct points \(P\left(x_1,\ y_1,\ z_1\right)\) and \(Q\left(x_2,\ y_2,\ z_2\right)\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Write parametric equations for the line through the distinct points \(P\left(x_1,\ y_1,\ z_1\right)\) and \(Q\left(x_2,\ y_2,\ z_2\right)\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Generalizing the Distance Formula Prove that the distance d(P, Q) between the points \(P\left(x_1,\ y_1,\ z_1\right)\) and \(Q\left(x_2,\ y_2,\ z_2\right)\) in space is \(\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}}\) by using the point \(R\left(x_2,\

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Generalizing a Property of the Dot Product Prove \(\mathbf{u} \cdot \mathbf{u}=|\mathbf{u}|^{2}\) where u is a vector in three-dimensional space.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False \(x^{2}+4 y^{2}=1\) represents a surface in space. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The parametric equations x = 1 + 0t, y = 2 - 0t, z = -5 + 0t represent a line in space. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, you may use a graphing calculator to solve the problem. Multiple Choice A first-degree equation in three variables graphs as (A) a line. (B) a plane. (C) a sphere. (D) a paraboloid. (E) an ellipsoid.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, you may use a graphing calculator to solve the problem. Multiple Choice Which of the following is not a quadric surface? (A) A plane (B) A sphere (C) An ellipsoid (D) An elliptic paraboloid (E) A hyperbolic paraboloid

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, you may use a graphing calculator to solve the problem. Multiple Choice If v and w are vectors and c is a scalar, which of these is a scalar? (A) v + w (B) v - w (C) \(\mathbf{v} \cdot \mathbf{w}\) (D) cv (E) |v|w

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, you may use a graphing calculator to solve the problem. Multiple Choice The parametric form of the line \(\mathbf{r}=\langle 2,-3,0\rangle+t\langle 1,0,-1\rangle\) is (A) x = 2 - 3t, y = 0 + 1t, z = 0 - 1t. (B) x = 2t, y = -3 + 0t, z = 0 - 1t. (C) x = 1 + 2t, y = 0

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Writing to Learn The figure shows a graph of the ellipsoid \(x^{2} / 9+y^{2} / 4+z^{2} / 16=1\) drawn in a box using Mathematica computer software. (a) Describe its cross sections in each of the three coordinate planes, that is, for z = 0, y = 0, and x = 0. In your description, inc

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Revisiting Example 6 Read Example 6. Then using v = 193.88i + 22.63j + 125k, establish the following: (a) The planes compass bearing is \(83.34^{\circ}\). (b) Its speed downrange (that is, ignoring the vertical component) is 195.2 mph. (c) The plane is climbing at an angle of \(32.63^{\ci

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The cross product \(\mathbf{u} \times \mathbf{v}\) of the vectors \(\mathbf{u}=u_{1} \mathbf{i}+u_{2} \mathbf{j}+u_{3} \mathbf{k}\) and \(\mathbf{v}=v_{1} \mathbf{i}+v_{2} \mathbf{j}+v_{3} \mathbf{k}\) is \(\mathbf{u} \times \mathbf{v}=\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k}

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The cross product \(\mathbf{u} \times \mathbf{v}\) of the vectors \(\mathbf{u}=u_{1} \mathbf{i}+u_{2} \mathbf{j}+u_{3} \mathbf{k}\) and \(\mathbf{v}=v_{1} \mathbf{i}+v_{2} \mathbf{j}+v_{3} \mathbf{k}\) is \(\mathbf{u} \times \mathbf{v}=\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k}

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The cross product \(\mathbf{u} \times \mathbf{v}\) of the vectors \(\mathbf{u}=u_{1} \mathbf{i}+u_{2} \mathbf{j}+u_{3} \mathbf{k}\) and \(\mathbf{v}=v_{1} \mathbf{i}+v_{2} \mathbf{j}+v_{3} \mathbf{k}\) is \(\mathbf{u} \times \mathbf{v}=\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k}

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The cross product \(\mathbf{u} \times \mathbf{v}\) of the vectors \(\mathbf{u}=u_{1} \mathbf{i}+u_{2} \mathbf{j}+u_{3} \mathbf{k}\) and \(\mathbf{v}=v_{1} \mathbf{i}+v_{2} \mathbf{j}+v_{3} \mathbf{k}\) is \(\mathbf{u} \times \mathbf{v}=\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k}