At which point P does the curve r(t) = ( 2t+3, 3t², t* ) given in vector form have the tangent vector (2, -6, – 4) ? (a) P(5, 3,1) (b) P( 3, 0, 0) (c) P(1,3,1) (d) P(7,12, 16) (e) P(2, 3,1)

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 unit vector that is normal to the level curve of the function f(x, y) = 3x + 6y at the point…

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Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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Q: Two unit vectors that are parallel to the tangent line to the curve y= 2sinx at the point (t/6, 1)…

A: To solve the given question , we must know the slope of the tangent line to the curve y=2sinx at…

Q: .3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2)…

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1                now differentiate with respect…

Q: Find a vector function that represents the curve of intersection of the paraboloid z = 7(x^2) +…

A: We have to find vector function that represents the curve of intersection of the paraboloid z =…

Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

A:

Q: Find the directional derivative of f(r, y, z) = yr + z* at the point (2, 3, 1) in the direction of a…

A: Directional Derivative of a Function of Three Variables =>Directional derivative of  f ( x , y ,…

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: Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)

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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: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

A:

Q: A particle moves in a path defined by vector-valued fanction FH)= (4)i +(zt-3)j + ( 3t - 3t) K ,…

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Q: At which point P does the curve r(t) =( 2t2, 4t+1, t³ ) given in vector form have the tangent vector…

A: Given, r(t)→=2t2,4t+1,t3  tangent vector 4,4,3 we know derivative of vector valued function gives…

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: An object moves with velocity vector (t,t?,-t) starting at (1,2,3) when t=0. Find the function r…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

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: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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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 a vector tangent to the curve of intersection of the two cyclinders x2 + y? = 8 and y? + 22 = 8…

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Q: Find a vector parametrization of the circle of radius 3 in the xy-plane, centered at (4, -1),…

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Q: Two plane curves are defined by the vector functions r1(t)=⟨t,2t−4⟩ and r2(u)=⟨2u,u2⟩. Find the…

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Q: a)What is the slope of the tangent line to the curve y=2sin4x  at x=⊼(pie)/4? b) Find a unit vector…

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Q: Two plane curves are defined by the vector functions r1 (t) = (t, 2t – 4) and r2 (u) = (2u, u²).…

A: r1t=t,2t-4 and r2u=2u,u2 For the intersection point, t=2u   ...1u=t22t-4=u2    ...2 Convert the…

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: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector…

A: According to the given information, it is required to find the directional derivative.

Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: Find equations of the normal line and the tangent plane to the parametric surface defined by the…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  compare coordinate on…

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Find a vector tangent to the curve of intersection of the two cyclinders x² + y? = 2 and y? + z² = 2…

A: To find a vector tangent to the curve of intersection of two cylinders        x2+y2=2 and…

Q: Find the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: Find the directional derivative of f(x,y,z)=xeY+ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines I am solving only first question please resubmit other question.  To find…

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: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic  = Vector

Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88).…

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Q: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

Q: The path r(t) = (t- sin t) i+ (1- cos t) j describes motion on the cycloid x=t- sin t, y=1- cos t.…

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Q: Find the point on the graph of z = 2x^2 − 3y^2 at which vector n=⟨8,−12,1⟩ is normal to the tangent…

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: Q1) Find equation of plane normal to vector 3i + 2j – k and pass through point (1,1,5).

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Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

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: At which point P does the curve r(t)=( 2t³, 21², 3t – 1) givenin vector form have the tangent vector…

A: According to the problem, we have

Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.