Question 1 Let S be the surface that is the part of the plane x + y + z the first octant. Find a parametrization for S of the form r (x, y), where (x, y) E R and R is a suitable triangle in the xy-plane. 3 lying in

Q: Suppose we have a quadric surface described by 1 (r, y, z) | 1 1 = 7. 1 -4 Using canonical…

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Q: 5. Let U be the part of the hyperboloid x2 + y? + 2 = 2z2 shown below that lies below the plane z =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. The point (1, k, 4) lies on the plane [x, y, z] = [1, 2, 0] + s[3, 0, 1] + t[2, −1, 1]. Find the…

A: Given point (1,k,4) is on plane.plane  is

Q: -Determine the equation of the trace of this plane in the xz plane given 2x + y − z = 4.…

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Q: Find a parametric representation for the surface. the part of the sphere x² + y² + z² = 16 that lies…

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Q: 5 me cap of the sphere x² + y² + z² =25, for 2 ≤z≤5

A: Given equation is x2+y2+z2=25 for 52≤z≤5.

Q: Show that Þ(u, v) = (2u + 6, u — v, 3u + v) parametrizes the plane 2x - y - z = 12. Then: (a)…

A: Given, Φ(u,v) = (2u+6, u-v, 3u+v) The plane 2x - y - z = 12

Q: Consider the triangle T with points A = (1,0, 1), B= (1, 1, 2), C = (-1,2, 2). 1. Compute the area…

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Q: Find a point on the upside down elliptic paraboloid x² +4y2 + z = 1 where the tangent plane is…

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Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

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Q: 2) Find parametric representations for the following surfaces: a) S: the portion of the plane that…

A: We shall solve both the parts. We will make use of the formula for the plane passing through three…

Q: i-2yj + (z+3)k and suppose the outward flux of F through Side A is 1 and through Side B is -3. Can…

A: answer is in next step

Q: Question 1 Evaluate ff, A.n ds, where A = (x+ y²)i - 2xý + 2yzk and S is the surface of the plane 2x…

A: We find out given integral. Follow 2nd,3rd and 4th step.

Q: Show that (u, v) = (5u+5, uv, 9u + v) parametrizes the plane 2x - y -z = 10. Then: (a) Calculate T₁,…

A: Partial Differentiation:

Q: Find a parametric representation for the surface. the part of the sphere x² + y² + z² = 16 that lies…

A: x2+y2+z2=16 The part of the sphere lie between the plane z=0 and z=23

Q: ify Stokes' theor d S is the surface

A: INTRODUCTION: Stoke's Theorem:-…

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: Consider the surface given by the parametric vector function (image)   1. The graph of r (u, v) is…

A: Given : a surface given by the parametric vector function ru, v=sinucosvi→+sinusinvj→+sin2ucosvk→…

Q: quation of the plane p containing the point P(3,1,1)and normal to the line l which has parametric…

A: we have to find the equation of the plane containing the point P(3,1,1). and normal to the plane is…

Q: Q4, please show work and show work in simplest way possible. Thanks.

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the surface area of the part of the plane z=6+3z + 7y that lies above the rectangle [1, 6] x…

A: For the given surface z=6+3x+7y  the rectangle [1,6]x[0,6] To find the surface under the z and above…

Q: 2a + 6zy + 2y + 3z2 = 1. You are given that in canonical coordinates, the same surface is described…

A: The given surface 2x2+6xy+2y2+3z2=1 can be written as 1=x y z230320003xyz Let A=230320003 In…

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: (a) Suppose that the intersection of two surfaces F(x, y, z) = 0 and G(x, y, z) = 0 is a curve C.…

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Q: x= s+i The parametric equations of a plane are y=1+i. Find a scalar equation of the plane. z= 1-s a)…

A: The given parametric equations are: x=s+ty=1+tz=1-s