Find the vector of velocity which has a speed of (90m/sec) and parallel to the vector joining the two points P(2,1,3) and Q(1,2,1).

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

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Q: A vector with magnitude 7 points in a direction 145 degrees counterclockwise from the positive x…

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Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

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Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

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 a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

A: The vector parametrization is:                                       r(t) = r0 + tv = x0,y0,z0 +…

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

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

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= 6 sin 2t and 0 = 4t v=u, +Due…

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Q: Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ,…

A: Consider that: rθ=sin θ, cos θ, cos 3θ at θ=π3. Velocity vector denoted by vθ is vθ=r'θ.  Calculate…

Q: Consider a particle that moves around a circle. Is the velocity vector of the particle always…

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Q: give the position vectors of particles moving alongvarious curves in the xy-plane. In each case,…

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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: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(: OS…

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: Find the velocity vector in terms of u, and ue- T=2 cos 2t and 0= 4t %3D O A. v= (4 sin 2t)u, + (8…

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Q: A bullet is fired into the air with an initial velocity of 950 feet per second at an angle of 67o67o…

A: Given: A bullet is fired into the air with an initial velocity of 950 feet per second at an angle of…

Q: Find the directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: A point, p, is moving with acceleration 6t j -k at time t. If at t 1, the coordinates of P are (1,…

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Q: Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

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

A: Topic:- application of derivatives

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: Suppose the pathogen is currently at location (1, 1) in antigenic space. Using a vector projection,…

A: We have to determine the vector that specifies the velocity at which the pathogen is evolving…

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

A: Recall:The velocity is given by      v =r' ur +(rθ') uθandThe accerleration is given by     a…

Q: It is known that the acceleration vector for a particle is given by A(t) = 4j + 2tk. Determine the…

A: We need to determine vector equation of curve traced.

Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=<0,-2,1>Hence, Vector…

Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* –…

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Q: 9. Which is traveling faster, a car whose velocity vector is 217 +35j or a car whose velocity vector…

A: We are authorised to solve only one question, please repost remaining questions Magnitude of vector

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 two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the…

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Q: Find the Directional Derivabive of Pary,2)= x-yz'+ at the point CI, -2, 0) in the direcbion of…

A: A scalar function is a rule to associate a number to a particular point in space. The directional…

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3

A: Velocity is defined as the rate of displacement. Acceleration is known as the rate of change in…

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

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Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by < t^2+1, ln(2t+3) > for all t>=0

Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

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

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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: A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

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Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

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: Write the vector A = 2z1-xi + yk in cylindrical coordinates.

A: *concept:- cylindrical co-ordinate = (x, y, z).

Q: A vector with magnitude 4 points in a direction 265 degrees counterclockwise from the positive x…

A: Given  Magnitude of 4 points at an angle of 265° In counter clockwise direction  from positive x-…

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

Q: Find the velocity and acceleration vectors for the motion described by x = 4 – 3t2, y = 4 – 5t, z= 9…

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Q: Find the velocity vector for the position vector r(t) = (sin(3t), 10t°, e -"). x component = y…

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