For the given vector function below, find the equation of the plane that contains the osculating circle at t = 1 r(t) = %3D X- z = 0 x + z =2 с. х-2z%3D -1 а. b. d. 2x - z = 1 е. 3x - z =2

Q: Find a unit vector that is parallel to the line tangent to the parabola y = x2 at the point (6, 36).

A: The parabola y = x2 and the point (6, 36)

Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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Q: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= 5e a0 and = 1 dt v-Du, +Duo

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Q: Find the unit tangent vector for the vector function : r(t) = (t2 + 1,3 t, t3> %3D (1+4t2+9t)3…

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Q: The jet stream is blowing at 60 miles per hour in the direction N45°E. Express its velocity as a…

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Q: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

Q: Find a unit vector in the direction in which f (x, y) = 4 – 4:x² – 4y? decreases most rapidly at…

A: The direction in which the function  f(x,y)=4-4x2-4y2 is -∇f(x,y).

Q: Find the positive value for which the vector r(t) (2t, 9t?, 10t2 – 2) is perpendicular to r'(t). -

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Q: Find the velocity and acceleration vectors for the motion described by x = 6 + 4f², y= 6 + 4t², z =…

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Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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Q: Find the length of the curve with the given vector equation. r(t) = 2t 4 1 + 11t j+ 10t 4 k, -1 sts…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 3 and…

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Q: Consider the vector function      r(t) =〈t^2 - t, t^2 + t, t^3〉 Find equation of three different…

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Q: The vector equation for the curve of intersection of the surfaces x = y² and z = y in terms of the…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: the vectors y₁, y₂, Y3 (where y; E R² V i) must be linearly dependent?

A: Given the vectors y1, y2 and y3 in the vector space R3.

Q: Find a vector normal to the plane with the given equation.3(x − 4) − 8(y − 1) + 11z = 0

A: Consider the equation of the plane: 3x-4-8y-1+11z=0.   If equation of the plane has the form:…

Q: Find the vector equation that represents the curve of intersection of the paraboloid z 2x2 + y and…

A: z=2x2+y2  &amp; x=ey We can see that y can be represented in terms of x.

Q: (c) Find the vector equation of the line of intersection of the planes x-2y+z=0 and x+y=z= 1.

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r=5 sint and 0= 5t = (5 cost) u, +…

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Q: B) Find a vector parallel to the plane 2x – y – z = 4 and orthogonal to i +j+ k.

A: This is a problem of vector analysis.. we will solve the problem using the concept of vector dot…

Q: A velocity vector of v = 3t²i – 6t³ j – 4k L is governing the movement of an object in the 3D space.…

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Q: For the given vector function below, find the equation of the plane that contains the osculating…

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Q: Find a vector parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

A: Given:A plane 2x - y - z = 4 orthogonal to i + j + k

Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

A: The objective is to find the vector function that represents the curve of intersection of the two…

Q: For the given vector function below, find the equation of the plane that contains the osculating…

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Q: А. Find the domain of the vector position r(t) + t+2 (t + 2) j + In(9 – t²) k

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Q: Given the vector function 7 (t) = (3t, 5t", – 3t° + 2) - Find the velocity and acceleration vectors…

A: Given that vector function r→ t=3t,5t2,-3t5+2 To find the velocity and acceleration at t=-1Solution…

Q: B: The temperature at any point in circular metal plate centered at the origin is, T(x, y) = 100…

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Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: Given: The two surface equation: z = y2 and  x2 + y2 = 4

Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

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Q: Find the position vector for the particle with acceleration, initial velocity, and initial postion…

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Q: Find a vector n normal to the plane with the equation x+6y + 4z = -10. n= 00> (1₂)

A: Concept: The equation of the plane is written as: ax-x0+b(y-y0)+c(z-z0)=0 or ax+by+cz=d Here the…

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y?…

A: z = 4x2 + y2  ,  y = ex    We observe that the given two equations, here we can see that y can be be…

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= 6 sint and 0= 9t Ou, + (O ue V…

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Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

A: First, we will sketch the curve of the intersection of the surface. The equation of the surfaces are…

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

Q: The velocity of a particle is given in terms of the time t by v = sinti - 2cos(2t)j + t2k   where…

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Q: Sketch the curve of the vector function r(f) = ti +4costj, and indicate the orientation of the…

A: We have to sketch the curve of the vector function rt=ti+4costj, and to indicate the orientation of…