bartleby

Find a parametric representation for the surface: The plane through the origin that contains the vectors i - j and j - k. Hint: Let x, y, z be in terms of u and/or v.

Question

Find a parametric representation for the surface: The plane through the origin that contains the vectors i - j and j - k.

Hint: Let x, y, z be in terms of u and/or v.

Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
Not helpful? See similar books
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Systems Of Linear Equations. 8RQ
Learn more about
Coordinate Geometry
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: ). Find a parametric representation for the line of intersection of the following two planes: I - y…

A: We use cross product to find the direct vector for the line.

Q: Find a parametric representation for the surface. the part of the plane  z = x + 2  that lies inside…

A: We need to find parametric representation.

Q: Find the parametric representation for the surface with the given boundaries. The part of the sphere…

A: To find the parametric representation for the surface , x2 + y2 + z2 = 144 , that lies b/w the…

Q: Find a parametric representation of the line of intersection of the two given planes 2x+y-z=6…

A: Click to see the answer

Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface.…

A: Click to see the answer

Q: Determine whether the statement is true or false. If D is the disk given by x2 + y2 < 4, then I V4-…

A: Given the given relation is

Q: Write an equation of the tangent plane to the parametric surface: r(u, v) = (u + v)i + 3u^2j + (u −…

A: Click to see the answer

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: x2+y42+ z2=1,y=5x2+y42+ z2=1

Q: Identify the surface with the given vector equation. r(0,0) = 2sinocosei +2sinosinej +2/1+sin?ok a.…

A: The minimum number of parameters needed to represent a surface is two. Therefore, in general, the…

Q: Evaluate ⌠⌠(x+y)ds, where S is the cone whose parametric equations are x=ucosv, y=usinv, z=2u,…

A: Given  cone whose parametric equations are x=ucosv, y=usinv, z=2u, 0≤u≤3, 0≤v≤π/2 we find the given…

Q: Let F = (z,0. y) and let S be the oriented surface parametrized by (u, v) = (u² – v, u, v²) for 0 <…

A: (a) First, find the tangent vectors: Tu=∂ϕ∂u=2u,1,0Tv=∂ϕ∂v=−1,0,2v The vector N is the cross product…

Q: Express the area of the given surface as an iterated double inegral in polar coordiantes, and then…

A: We need to find the surface area in the portion of the sphere x^2+y^2+z^2=16 between the planes z=1…

Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface…

A: Click to see the answer

Q: Determine the intersection of the hyperbolic paraboloid z = (y2/b2) − (x2/a2) with the plane bx + ay…

A: Given The hyperbolic paraboloid equation is z=y2b2-x2a2 and the plane bx + ay − z = 0 .

Q: Consider the parametric surface S given by the portion of the sphere x +y² +z² = 4 where z 2 1.

A: In this question, we have to parameterize the surface in cartesian coordinates and then find the…

Q: Consider the surface with parametrization 7 (u, v) = (u, v, u² – v²). Fill in the blank to find the…

A: Click to see the answer

Q: Find constants a, b, c such that  G( u, v) = ( u + av, bu + v, 2u - c) parametrizes the plane 3x - 4…

A: Given G( u, v) = ( u + av, bu + v, 2u - c) parametrizes the plane 3x - 4 y + z = 5.

Q: Write the parametric equation of the bilinear surface corresponding to four points P(0 0)= 0.25 0…

A: Given coordinates are, P0,0=0.25,0P1,0=0.75,0P0,1=0.75,0.9P1,1=0.25,0.8 So, the parametric equation…

Q: If a parametric surface given by ri (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -3 <u < 3, –4 < v<…

A: We solve this

Q: The surface r(u,v)=(u,2v,3u – 4v) is a (a) cone. (b) plane. (c) sphere.

A: Given :The given surface is r(u,v)=&lt;u,2v,3u-4v&gt;To find:we have to check the given…

Q: Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 6) i+ (v³…

A: Click to see the answer

Q: Try to visualize the set of all points (x, y, z)in a coordinate space that are equidistant from the…

A: Click to see the answer

Q: (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 36 given the plane.

A: Click to see the answer

Q: Write an equation in general form of the tangent plane to the parametric surface at the stated…

A: Equation of tangent plane

Q: Consider the following equation of a plane in R³: -3z – 2y – 3z = -2 Convert your plane to vector…

A: Find the vector parametric form of the plane: -3x - 2y - 3z = -2

Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.

A: Click to see the answer

Q: Sketch the following Cartesian Products on the plane R? or in space {(x, y) € R²:x² + y² s 1} ×…

A: Click to see the answer

Q: Sketch the following Cartesian Products on the plane R? or in space IR. a. (-1,0, 2) x (1,2, 3) b.…

A: Click to see the answer

Q: Identify the surface Describe the surface with the given parametric representation. r(u, v) = ⟨u, v,…

A: Click to see the answer

Q: If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z =…

A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…

Q: Determine the constants a, B, y such that the surfaces ax?z – xy? = B, yaz – y² = 0, - intersect…

A: Click to see the answer

Q: Sketch the parametric surface x = (u^(2) + v^(2))^(1/2), y = u and z = v

A: It is surface of infinite CONE.

Q: 2 Sketch the parametric surface x = Vi u +v ,y = u, z = v.

A: We will sketch the parametric surface x=u2+v2, y=u, z=v. Notice that x2=u2+v2⇒x2=y2+z2.

Q: Write the sphere equationil odi lo anoitaupo ontemeeg bas Totoov bnif (d) x2 + y? + z2 + 2x - 4y –…

A: Click to see the answer

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y?…

A: z = 4x2 + y2  ,  y = ex    We observe that the given two equations, here we can see that y can be be…

Q: Please make sure its right. calc 3 Find a parametric representation for the part of the plane z = x…

A: Click to see the answer

Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: 1. Find a parametric representation for the surface: the part of the sphere x2 + y? + z2 = 4 that…

A: According to the given information, It is required to calculate the parametric representation for…

Q: a) Evaluate ds, where the curve C is the intersection between the surface z = V1- y? and the plane r…

A: Click to see the answer

Q: Let P(r, y, z) be the point at which the line with parametric equations x = -t, y=3+2t, z=1-t te R,…

A: Click to see the answer

Q: Which of the following represents a plane surface whose x-, y-, and z-intercepts are a, b, and c…

A: Given questions are solved.

Q: Identify the surface with the given vector equation. r(u,v) = (u + v)i + (3 – v)j + (2 + 4u + 6v)k…

A: Click to see the answer

Q: Find a parametric representation for the surface. The part of the plane  z = x + 2  that lies…

A: Given: The part of the plane  z = x + 2  that lies inside the cylinder  x2 + y2 = 9.

Q: a) Evaluate x²y? ds, where the curve C is the intersection between the surface z = := V1– y? and the…

A: Click to see the answer

Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, yz

A: Let the plane P whose equation is;                                      -x+y=4…

Q: Which of the following best describes the surface with the vector equation r(u, v) = (cos u)i + (sin…

A: Click to see the answer

Q: Let a, b and c be the last three digits of your student ID and let d=max(a,b,c). How many points are…

A: we have surface  z=6x2+y2 and plane 6x+y+z=0lets denote the surface equation as f(x,y,z)=z-6x2-y2and…

Q: Identify the surface with the given vector equation. 5. r(s,t) = &lt; s cos t, s sin t, s&gt;

A: The given vector equation is r(s,t)=s cos t , s sin t, s

Q: )الكــره the Sphere OThe Portion of planes z=l x +y+Z² = \6 between the %3D and z=2.

A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…

Q: find a parametrization of the surface. The paraboloid z = x2 + y2, z&lt;=4 The paraboloid z = 9 - x2…

A: Click to see the answer

Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Linear Algebra: A Modern Introduction
    Algebra
    ISBN:9781285463247
    Author:David Poole
    Publisher:Cengage Learning
    Elementary Geometry For College Students, 7e
    Geometry
    ISBN:9781337614085
    Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
    Publisher:Cengage,
    Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
  • Mathematics For Machine Technology
    Advanced Math
    ISBN:9781337798310
    Author:Peterson, John.
    Publisher:Cengage Learning,
    Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
  • Linear Algebra: A Modern Introduction
    Algebra
    ISBN:9781285463247
    Author:David Poole
    Publisher:Cengage Learning
    Elementary Geometry For College Students, 7e
    Geometry
    ISBN:9781337614085
    Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
    Publisher:Cengage,
    Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Mathematics For Machine Technology
    Advanced Math
    ISBN:9781337798310
    Author:Peterson, John.
    Publisher:Cengage Learning,
    Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning