Consider the curve F(1)=i +(/2 In(?))j + 1 -k. | а) Find the binormal vector B(1)

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y2 = 50 and y? + 22 =…

A: Find a vector tangent to the curve of intersection of the two cylinderx2+y2=50 and y2+z2=50 at the…

Q: Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t)…

A: Curve length problem..

Q: Find a vector-valued function whose graph is the indicated surface.

A: To find :               Find the vector valued function whose graph is the indicated surface.

Q: 6. A particle moves in the xy-plane in such a way that its velocity vector is (1+1, 1). If the…

A: Find the position vector

Q: Match the vector field with its graph. F(x, y) = yi 址 四 場 x Q 6 電

A: F(x,y)=yi So at any point vector magnitude is same as y-cooridnate Also, if y is negative [below the…

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A: A unit vector is a vector of length 1. Any nonzero vector can be divided by its length to form a…

Q: /Find the tangent and normal vector for curve r= (5sin n i+5 cos n j+n k) n=(In 2t)

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Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

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Q: Match the vector field with its graph. F(x, y) = yi KE y -5+

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Q: 1. Find one normal vector of the tangent plane to f(x, y) = cos(x² + y²) at point P(1, 1, cos 2).

A: Please check step 2 for the solution.

Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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Q: Find a vector parametrization of the curve x = -3z² in the xz-plane. t as the parameter in your…

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Q: Match the vector field with its graph. F(x, y) = yi 5 5 -5+ サ

A: To match the given vector field to its graph, where given graphs are given below.

Q: Find the normal vector to the tangent plane of z = 2u at the point (4,8,3) X component y component…

A: We need to find normal vector component.

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

Q: Match the vector field with its graph. F(x, y) = yi 1 |||||||||| 三 6 靈

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Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

Q: ind the directional derivative of the function f(x, y, z) = Vx² + y² + z² at point (2, -3, 6) in the…

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Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: Find a normal vector at point P. xy2 - 4x2 + y + 8x = 7, P(4, 3) Find a tangent vector at point P.

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Q: nd the directional derivative of the function f(z, Y) In(z +y) at the point (3, – 1) in the rection…

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Q: Prove that the tangent vector is always orthogonal tothe position vector for the vector-valued…

A: Given r(t) =⟨sin t, sint cos t, cos2 t⟩.  we need to prove that the tangent vector is always…

Q: Find the normal vector to the tangent plane of z = 4e"² - 6y at the point (12, 24, 4). x component y…

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Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve F(t)…

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Q: (A) Find A vector tangent and normal for the curve: x3 y = + 5 2 at the point (1, 5.5)

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

Q: Compute the vector assigned to the pointP = (−3, 5) by the vectorfield:(a) F(x, y) = (xy,y − x)(b)…

A: To Determine : (a) F(x, y) = (xy,y − x)(b) F(x, y) = (4, 8)(c) F(x, y) = 3x+y , log2(x + y) Given:…

Q: Thẻ nòrmal vector to the plane 3x + 4y – 5z – 6 = 0 is A 3i+ 4j – Sk B 3i + 4j + Sk C 3i+ 4j – 6k D…

A: It is normal vector form.

Q: Find the normal vector to the tangent plane of z = 6e- Öy at the point (12, 24, 6). x component = y…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

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Q: Find the normal vector to the tangent plane of z 7ea-2y at the point (4,8,7) x component = y…

A: The tangent plane is given as z=7ex2-2y and the point is (4,8,7) Let f(x,y,z)=7ex2-2y-z Then obtain…

Q: Compute the tangent vector to the given path. c(t) = (4t sin(t), 6t) %3D

A: The tangent vector for a vector r→t is r→'t.

Q: Find a vector parametrization of the curve z = :-222 in the xz-plane. Use t as the parameter in your…

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Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2.1,7",e-7) from 0 to…

A: The detailed solution of the problem is given in the next steps.

Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: Calculate the line integral of the vector field F = -2i+ 4jalong the line from the point (3,0) to…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 1信 -6 5 to -5+

A: We have to take point (x,y) and then draw vector field

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5 5 5 -5+ -5+

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Q: 16. Sketch the cycloid r(t) = (t- sint, 1 - cos t) together with its tangent vectors at t = and .…

A: Solved the above problem.

Q: Sketch some vectors in the vector field F(x, y) = 2xi + yj.

A: Given: F(x, y) = 2xi^ + yj^

Q: The largest value of the constant b such that the vector-valued function F(t) =< cos 21It, sin (t-…

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Q: (8) Find a vector parameterization of the line r(t) which passes through the point P = (1,2, –8)…

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Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2 t, e",e-) from 0 to…

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Q: Prove that the vector T'(t) = 0 for moving in a straight line

A: Note that, the object's path is rt=xti+ytj. yt=mxt+b, where m and b are constant. It is known that,…

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: (iii) Find a vector equation for the tangent line to the curve of intersection of the cylinder a² +…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

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