Consider a surface S which is parameterised by {r(u, v) = ui + (u + v)j+ vk :0 < u < 1,0 < v< 1}. At the point (,1, ), find a normal to S that has i component given by i itself. (Another way to say this: i. N = 1.) N = i+ • j+ • k

Consider a surface S which is parameterised by {r(u, v) = ui + (u + v)j+ vk :0 < u < 1,0 < v< 1}. At the point (,1, ), find a normal to S that has i component given by i itself. (Another way to say this: i. N = 1.) N = i+ • j+ • k

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: b such that the surf 4x2y + z3 = 4 cut -1 ?). %3D

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

A: Equation of a tangent to the surface z=f(x,y) at point (a,b,f(a,b)) is given by…

Q: Let S be the paraboloid y = x^2 + z^2. Find a parametric representation for S and its tangent plane…

A: The given data is: Let S be the paraboloid y=x2+z2 Find a parametric representation for S and its…

Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

Q: What is the tangent plane equation of sphere f(x, y. :)=x² + y² += =6 at point (1,-1,2)? O a.…

A: I hope that this solution will help you .Thankyou. Best regards.

Q: 8.) Find the planes tangent to the following surfaces indicated points: a:) x² + 2y ²2/3 X ² = 10₁…

Q: Consider the surface of equation z = x2 + y² . What is the equation for the tangent line to S at the…

A: We need to find equation of tangent line.

Q: Find the points on the hyperboloid of one sheet x² + 3y² − 5z² = 16 where the tangent plane is…

Q: Consider the equation of the surface S given by -2X“ - yPz° + xy = -4, where a is an odd number and…

Q: Show that the parametric curve r(t)= , t [-1,1] is smooth and compute its lengh

A: The given parametric curve is: r(t)=t1+t2, 11+t2 ; t∈-1, 1

Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

Q: Describe and sketch the surface given by the function.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: you know that a sphere has the equation of x^2 + y^2 +z^2 -6x +4z =3 are the following points…

A: The equation of sphere is:-Now add 9 and 4 both side:-

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

Q: Where does the plane tangent to z = At z = 5exy at (7, 7, 5) meet the z-axis?

A: We find equation of tangent plane to z=5e^(x-y) at (7,7,5)

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

A: For tangent plane of the surface f(x,y,z)=k at a given point normal vector to tangent plane will be…

Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

Q: Find T, N, and B for the curve r(t) = (14t, 14t, e') at (0, 0, 1). %3D Hint: After finding T', plug…

Q: y Consider the surface of equation z = X+Y² What is the equation for the tangent line to S at the…

A: This is a problem of vector calculus.

Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

Q: Describe all extensions of the identity map of ℚ to an isomorphism mapping ℚ(3rd root of 2) onto a…

Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

Question

Consider a surface S which is parameterised by
{r(u, v) = ui + (u + v)j + vk :0 <u< 1,0 <v< 1}.
At the point (, 1, }), find a normal to S that has i component given by i itself. (Another way
to say this: i. N = 1.)
N = i+
• j+
where the choices are:
(a) 1
(b)
(c) V3
(d) -V3
(e) *
(f)
(g) None of the other choices are correct
Find the integral of the scalar function f(x, y, z) = x over this surface
æ dS =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Find an equation of the tangent plane to the surface given implicitly by z = sin(xy) at the point (,-1, -). Lütfen birini seçin: a.5z – ny + 2z = 3n – 2 b.яz — у + 2: -т - 3 c.2/3z – 4ny – 2z = 3 d.3z ny + 6z = 27 – 3/3 e.-3z + ny + 2z = * - V3
C is the semicircular curve drawn in the ground (the xy-plane) joining the points (0, - 2), (2, 0), (0, 2). A fence is to be built along the curve planted at each point of C, going up in the positive z-direction, with a height at the point (x, y) given as h(x,y)= 1 + Find the area of the fence that will be built. In other words, work out the line integral h(x,y) ds The area of the fence is
Consider the equation хд,и — удуи —D —и with the initial condition: u(x, y) = 2 on the circle {(x, y) : x² + y? = 1}. Show that this PDE does not have any solution near the point (- , ,2).
Find the planes tangent to the following surfaces at the indicated points. x² + 2y² + 9xz = 12, at the point (1, 2, ¹-) 3 (a) (b) y² - x² = 8, at the point (1, 3, 7) (c) xyz = 1, at the point (1, 1, 1)
9.
5. Find the equation of the line tangent to the intersection of the surface z = arctan ry with the plane r = 2, at the point (2,, )