Let C1 be a curve defined by some vector function K with unit binormal B such that 3. 3 Ř(0) = (–2, 5, 4) , ř (7) = (4,0, 3) , and B(t) = ( cost, sir cost, - sin t, (a) Find the equation of the osculating plane to C1 at t = 0. (b) Find the unit normal vector to C1 at t = T (c) Evaluate (R · B)'(0).

Q: Let r(t) = t³ i + t² j + k be a space curve. Which of the following vectors is perpendicular to the…

A: The given curve is: r(t)=t3,t2,1tr'(t)=3t2,2t2,-1t2 Now, the given point is r(1). So, r'(1)=3,2,-1…

Q: A smooth curve C is defined by some vector function R(t) with R = (π,0,−2) and R'(t) = (2, √√5 csc…

A: Since you have asked multiple questions, we will solve the Question Q (1) and (2) for you. If you…

Q: Sketch the graph of the plane curve . r(t) = ti − t3j and sketch the vectorsT(t) and N(t) at the…

A: Here we are taking the T(t) as the tangent vector and N(t) as the Normal vector Consider the…

Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder + (y − 1)² = 1 (a)…

A: We will use the basic knowledge of vector calculus and differential calculus to answer all three…

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j+ sin(rt) k. %3D…

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Q: Find all values of t for which the tangent line to the curve r(t) = (2t – t,t - t²) is orthogonal to…

A: Find the solution below

Q: Find the principle unit normal vector to the curve given below at the specified point. r(t) =…

A: That's easy, check calculations. Have a great day!!!

Q: The length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the…

A: Given information: Parametric equation of curve is : x=x(t)y=y(t)z=z(t) We need to find the length…

Q: Let F(x, y, z) = xye" – 2° Ja and P(1,0, –1). Let S be the surface defined by the equation xye" –…

A:

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve 7(t)…

A: We will find out the required value.

Q: A space curve is given by the vector function r(t) = (3t, t² + 6t, t³ ). Then the unit tangent…

A: GIVEN: r(t) = {3t, t2 + 6t, t3}

Q: Let C be the curve with parametrization r(t) : ,0 . Find the value of F · dr.

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Q: Find the unit tangent vector T and the principal unit normal vector N for the following…

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Q: Let r (t ) = sin t i + et j + In (t + 1) k be a space curve. Which of the following vectors is…

A:

Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

A:

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(zt) î + at j+ sin(rt) k. %3D…

A:

Q: (a) Consider the curve C : r(t) = [t , –t², 2– t²]. Find a tangent vector, a unit tangent vector and…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let C, be a curve defined by some vector function R with unit binormal B such that 3 Ř(0) = (-2,5,…

A: For calculating the osculating plane we use the fact that the binormal is also the normal to the…

Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

A:

Q: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

A: We will find equation of common curve and parametrize it to find vector equation of C and the use…

Q: Consider the curve G given by the vector function f(t) = tỉ + tj + (2 +t²)k where t e [0,4]. Give an…

A:

Q: (A) Given the vector function r(t)=( V21,e', e-), the unit normal vector N(t) is of the %3D form:…

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

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 3, 11) for the function…

A: The unit vector normal to the surface f(x, y, z)=0 is ∇f∇f. where ∇f = fx, fy, fz and ∇f = fx2 + fy2…

Q: Find all values of t for which the tangent line to the curve r(t) = (3t – t°,t –- t²) is orthogonal…

A: Given curve is

Q: Let C be a curve defined by some vector function R with unit binormal B such that R(0) = (-2, 5, 4)…

A: Given C1 is a curve defined by some vector function R→ with unit binormal B→ such that R→(0)=-2,5,4,…

Q: Let be a curve defined by the vector function (t)= 6ti + çin 2t -cos 2+ k 3- and Find the moving…

A: Let C1 be a curve defined by the vector function R→(t)=6ti→+sin2tj→-cos2tk→. Find the moving…

Q: Let f(r.y) = r'y- Find a unit vector tangent to the level curve f(r, y) = 3 at its point (1,2).

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Q: 2. Consider the curve traced out by the vector valued function r(t) = (sin t cos t, cos? t, sin t)…

A: given that r(t)=(sintcost,cos2t,sint) we need to show that the curve lines on the surface of the…

Q: Sketch the space curve represented by the vector-valued function and give the orientation of the…

A: Explanation:

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: 4. (a) Find the mid-point, unit tangent vector and unit normal vector at the mid-point of a planar…

A:

Q: Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the…

A: To find: The normal vector of the tangent plane to the surface at the given point. Given…

Q: Let C be the curve of intersection of the surfaces with equations   x2 + y  =  5   and   24x + 4y…

A: Given: Let C be the curve of intersection of the surfaces with equations x2+y=5  and   24x + 4y + z…

Q: Let r (t ) sin t i + etj + ln (t + 1) k be a space curve. Which of the following vectors is…

A:

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: Here we use the concept of gradient of a scalar function at given point.

Q: Let r (t) = ti + e2t j + t³ k be a space curve. Which of the following vectors is perpendicular to…

A:

Q: Suppose r(t) is a vector function in R3 Show that if r(t)is perpendicular to the tangent vector…

A: Suppose that the position vector r→t be, r→t=ft,gt,ht…

Q: Let C be the portion of the parabola y = x², oriented from the starting point (0,0) towards the end…

A:

Q: 5. Find the unit tangent vector, the unit normal vector and the binormal vector to the curve r(t) =…

A: The given vector curve is:  r→(t)=t3,t2,t Given point is: (1, 1, 1). Therefore t = 1. Now the Unit…

Q: Let r(t ) = t³i + t? j + k be a space curve. Which of the following vectors is perpendicular to the…

A:

Q: A smooth curve C is defined by some vector function R(t) with R() = (7,0,-2) and R' (t) = (2, √5…

A:

Q: Let r (t) = ti + e2t j + t3 k be a space curve. Which of the following vectors is perpendicular to…

A:

Q: Sketch the plane curve represented by the vector valued function and give the orientation of the…

A: Given rt=t3i+t2j.

Q: A smooth curve C is defined by some vector function R(t) with R (7) 2 = = (π,0,−2) and R' (t) = (2,…

A:

Q: Match the vector-valued functions (a)-(f) with the space curves- (1)–(vi) in Figure 10. (a) r(1) =…

A: (d) Identify the graph of the vector function rt=cos3t, sin3t, sin 2t. From the function, it…

Q: Show that the vector-valued function r(t) = e−t cos ti + e−t sin tj + e−t k  lies on the cone z2 =…

A: Given vector valued function is r(t)=e-tcosti+e-tsintj+e-tk.

Q: Match the vector-valued functions (a)–(f) with the space curves (1)–(vi) in Figure 10. (a) r(1) = (t…

A: (d) map to  (vi) (e)  maps to (iv) (f) map to (iii)

Q: Let r (t ) = t i + e2t j + t³ k be a space curve. Which of the following vectors is perpendicular to…

A: Solve the following