New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
mathematics
calculus 4th
Calculus 4th Edition Jon Rogawski, Colin Adams, Robert Franzosa - Solutions
Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5, xz
Find the trace of the plane in the given coordinate plane.3x + 4z = −2, xy
Find the trace of the plane in the given coordinate plane.3x + 4z = −2, xz
Find the trace of the plane in the given coordinate plane.−x + y = 4, xz
Find the trace of the plane in the given coordinate plane.−x + y = 4, yz
Does the plane x = 5 have a trace in the yz-plane? Explain.
Give equations for two distinct planes whose trace in the xy-plane has equation 4x + 3y = 8.
Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z.
Find parametric equations for the line through P0 = (3, −1, 1) perpendicular to the plane 3x + 5y − 7z = 29.
Find all planes in R3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.
Find all planes in R3 whose intersection with the xy-plane is the line r(t) = t(2, 1, 0).
Compute the angle between the two planes, defined as the angle θ (between 0 and π) between their normal vectors (Figure 10).Planes with normals n1 = (1, 2, 1), n2 = (4, 1, 3) n 112 n2 0 n PL P 0 L
Compute the angle between the two planes, defined as the angle θ (between 0 and π) between their normal vectors (Figure 10).2x + 3y + 7z = 2 and 4x − 2y + 2z = 4 n 112 n2 0 n PL P 0 L
Compute the angle between the two planes, defined as the angle θ (between 0 and π) between their normal vectors (Figure 10).3(x − 1) − 5y + 2(z − 12) = 0 and the plane with normal n = (1, 0, 1) n 112 n2 0 n PL P 0 L
Compute the angle between the two planes, defined as the angle θ (between 0 and π) between their normal vectors (Figure 10).x − 3y + z = 3 and 2x − 3z = 4 n 112 n2 0 n PL P 0 L
Compute the angle between the two planes, defined as the angle θ (between 0 and π) between their normal vectors (Figure 10).The plane through (1, 0, 0), (0, 1, 0), and (0, 0, 1) and the yz-plane n 112 n2 0 n PL P 0 L
Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2.
Let P1 and P2 be planes with normal vectors n1 and n2. Assume that the planes are not parallel, and let L be their intersection (a line). Show that n1 × n2 is a direction vector for L.
Find a plane that is perpendicular to the two planes x + y = 3 and x + 2y − z = 4.
Let L be the intersection of the planes x + y + z = 1 and x + 2y + 3z = 1. Use Exercise 64 to find a direction vector for L. Then find a point P on L by inspection, and write down the parametric equations for L.
Let L denote the intersection of the planes x − y − z = 1 and 2x + 3y + z = 2. Find parametric equations for the line L. To find a point on L, substitute an arbitrary value for z (say, z = 2) and then solve the resulting pair of equations for x and y.
Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1.
The planeintersects the x-, y-, and z-axes in points P, Q, and R. Find the area of the triangle ΔPQR. || NIM + + XIN
In this exercise, we show that the orthogonal distance D from the plane P with equation ax + by + cz = d to the origin O is equal to (Figure 11) D = |d| a + b + c
Two vectors v and w, each of length 12, lie in the plane x + 2y − 2z = 0. The angle between v and w is π/6. This information determines v × w up to a sign ±1. What are the two possible values of v × w?
Let P be a plane with equation ax + by + cz = d and normal vector n = (a, b, c). For any point Q, there is a unique point P on P that is closest to Q, and is such that PQ is orthogonal to P(Figure 12).Show that the point P on P closest to Q is determined by the equation Z 0 Q n P P X
By definition, the distance from Q = (x1, y1, z1) to the plane P is the distance to the point P on P closest to Q. Prove distance from Q to P= lax + by + cz - dl ||n||
Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x + y + z = 1. OP=00+ d-00 n n.n n
Use Eq. (6) to find the distance from Q = (1, 1, 1) to the plane 2x + y + 5z = 2. distance from Q to P = lax + by + cz - d| ||n||
Find the point P nearest to Q = (−1, 3, −1) on the plane x − 4z = 2.
Find the distance from Q = (1, 2, 2) to the plane n · (x, y, z) = 3, where n = (3/5,, 4/5, 0).
What is the distance from Q = (a, b, c) to the plane x = 0? Visualize your answer geometrically and explain without computation. Then verify that Eq. (6) yields the same answer.
The equation of a plane n · (x, y, z) = d is said to be in normal form if n is a unit vector. Show that in this case, |d| is the distance from the plane to the origin. Write the equation of the plane 4x − 2y + 4z = 24 in normal form.
Convert from cylindrical to rectangular coordinates. 2, -8) 3'
Convert from cylindrical to rectangular coordinates.(4, π, 4)
Convert from cylindrical to rectangular coordinates. klin 5' 2,
Convert from cylindrical to rectangular coordinates. (1,77,-2)
Convert from rectangular to cylindrical coordinates.(1, −1, 1)
Convert from rectangular to cylindrical coordinates.(2, 2, 1)
Convert from rectangular to cylindrical coordinates. 3 3V3 2 2
Convert from rectangular to cylindrical coordinates.(1,√3, 7)
Convert from rectangular to cylindrical coordinates. 5 5 2 2 ,2
Convert from rectangular to cylindrical coordinates.(3, 3 √3, 2)
Describe the set in cylindrical coordinates.x2 + y2 ≤ 3
Describe the set in cylindrical coordinates.x2 + y2 + z2 ≤ 10
Describe the set in cylindrical coordinates.y2 + z2 ≤ 4, x = 0
Describe the set in cylindrical coordinates.x2 + y2 + z2 = 9, y ≥ 0, z ≥ 0
Describe the set in cylindrical coordinates.x2 + y2 ≤ 9, x ≥ y
Describe the set in cylindrical coordinates.y2 + z2 ≤ 9, x ≥ y
Sketch the set (described in cylindrical coordinates).r = 4
Sketch the set (described in cylindrical coordinates).θ = π/3
Sketch the set (described in cylindrical coordinates).z = −2
Sketch the set (described in cylindrical coordinates).r = 2, z = 3
Sketch the set (described in cylindrical coordinates).1 ≤ r ≤ 3, 0 ≤ z ≤ 4
Sketch the set (described in cylindrical coordinates).z = r
Sketch the set (described in cylindrical coordinates).r = sin θ
Sketch the set (described in cylindrical coordinates).1 ≤ r ≤ 3, 0 ≤ θ ≤ π/2, 0≤ z ≤ 4
Sketch the set (described in cylindrical coordinates).z2 + r2 ≤ 4
Sketch the set (described in cylindrical coordinates).r ≤ 3, π ≤ θ ≤ 3π/2, z = 4
Find an equation of the form r = ƒ(θ, z) in cylindrical coordinates for the following surfaces.z = x + y
Find an equation of the form r = ƒ(θ, z) in cylindrical coordinates for the following surfaces.x2 + y2 + z2 = 2
Find an equation of the form r = ƒ(θ, z) in cylindrical coordinates for the following surfaces.x2/yz = 1
Find an equation of the form r = ƒ(θ, z) in cylindrical coordinates for the following surfaces.x2 − y2 = 4
Find an equation of the form r = ƒ(θ, z) in cylindrical coordinates for the following surfaces.x2 + y2 = 4
Convert from spherical to rectangular coordinates. (3,0,
Convert from spherical to rectangular coordinates. -3 -4
Find an equation of the form r = ƒ(θ, z) in cylindrical coordinates for the following surfaces.z = 3xy
Convert from spherical to rectangular coordinates. 3 4
Convert from spherical to rectangular coordinates.(3, π, 0)
Convert from spherical to rectangular coordinates. 6, 5 6' 6
Convert from spherical to rectangular coordinates.(0.5, 3.7, 2)
Convert from rectangular to spherical coordinates. V3 3 2 2
Convert from rectangular to spherical coordinates.(√3, 0, 1)
Convert from rectangular to spherical coordinates.(1, 1, 1)
Convert from rectangular to spherical coordinates. 2 V3 2
Convert from rectangular to spherical coordinates.(1, −1, 1)
Convert from rectangular to spherical coordinates. 2 2 2 2
Convert from cylindrical to spherical coordinates.(2, 0, 2)
Convert from cylindrical to spherical coordinates.(3, π,√3)
Convert from spherical to cylindrical coordinates.(4, 0, π/4)
Convert from spherical to cylindrical coordinates.(2, π/3, π/6)
Describe the given set in spherical coordinates.x2 + y2 + z2 ≤ 100
Describe the given set in spherical coordinates.x2 + y2 + z2 = 1, z ≥ 0
Describe the given set in spherical coordinates.x2 + y2 + z2 = 10, x ≥ 0, y ≥ 0, z ≥ 0
Describe the given set in spherical coordinates.x2 + y2 + z2 ≤ 1, x = y, x ≥ 0, y ≥ 0
Describe the given set in spherical coordinates.y2 + z2 ≤ 4, x = 0
Describe the given set in spherical coordinates.x2 + y2 = 3z2
Sketch the set of points (described in spherical coordinates).ρ = 4
Sketch the set of points (described in spherical coordinates).ϕ = π/4
Sketch the set of points (described in spherical coordinates).ρ = 2, θ = π/4
Sketch the set of points (described in spherical coordinates).ρ = 2, ϕ = π/4
Sketch the set of points (described in spherical coordinates). 0 = 2 = 4 1
Sketch the set of points (described in spherical coordinates).ρ = 2, 0 ≤ ϕ ≤ π/2
Sketch the set of points (described in spherical coordinates). 0522 2 OST P2, 0 0
Sketch the set of points (described in spherical coordinates). p = 1, 3 < < 27 3
Sketch the set of points (described in spherical coordinates).ρ = csc ϕ
Sketch the set of points (described in spherical coordinates).ρ = csc ϕ cot ϕ
Find an equation of the form ρ = ƒ(θ, φ) in spherical coordinates for the following surfaces.x2 + y2 = 9
Find an equation of the form ρ = ƒ(θ, φ) in spherical coordinates for the following surfaces.x = 3
Find an equation of the form ρ = ƒ(θ, φ) in spherical coordinates for the following surfaces.z = 2
Showing 2200 - 2300
of 8339
First
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Last
Step by Step Answers
Get 50% OFF
Claim Now
![distance from Q to P = lax+by+cz -d] ||n||](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1704/1/9/0/3676593e19f35b021704190367122.jpg)
