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.
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…
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Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface.…
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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 −…
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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…
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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…
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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)=<u,2v,3u-4v>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…
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Q: Try to visualize the set of all points (x, y, z)in a coordinate space that are equidistant from the…
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Q: (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 36 given the plane.
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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.
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Q: Sketch the following Cartesian Products on the plane R? or in space {(x, y) € R²:x² + y² s 1} ×…
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Q: Sketch the following Cartesian Products on the plane R? or in space IR. a. (-1,0, 2) x (1,2, 3) b.…
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Q: Identify the surface Describe the surface with the given parametric representation. r(u, v) = ⟨u, v,…
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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…
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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 –…
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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…
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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…
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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,…
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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…
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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…
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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…
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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) = < s cos t, s sin t, s>
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<=4 The paraboloid z = 9 - x2…
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