1. Find a parametrization for the line segment from (2, 1, 3) to (4,3, 2). 2. Find the velocity and the speed of a particle whose motion is given by F(t) = ((t – 1)°, 2, 2t³ – 3t²) at time t = 2.

Q: If a particle moves in the xy-plane so that at time t > 0 its position vector is (In (t2 + 2t) ,…

A: As we know that the expression for the velocity is; v=dstdt Given position vector is:…

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Q: a. Find a parametrization of the curve x = (y* – 3)e2y.

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

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Q: 4. Let r(t) = (t)i + (t-16t²) ; be the position of a particle in a plane at time t. Find the angle…

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Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

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A: Given  a t=4t,5 sint, cos 3twe know that,v→t=∫a t dt +C1r t=∫vt  dt  +C2 ∴v→t=∫4t, 5 sint, cos 3t…

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Q: find a parametrization c(t) of the curve satisfying the given condition.  y = x 2, c(0) = (3, 9)

A: The given function is y=x2 and c(0) =(3,9) Let x(0) =3 and y(0)= 9 Take x =t +x(0) Thus, x = t+3

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A: The objective of the question is determine the length of the curve.

Q: Evaluate | (3z2 – 22) dz, where C is parametrized by z(t) = t+iť, 0<t< 1. -

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A: Given:

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A: Introduction: A very important aspect of vector calculus is the parametrization. the line integral…

Q: find a parametrization c(t) of the curve satisfying the given condition. y = 3x − 4, c(0) = (2, 2)

A: It is given that,

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A: Answer

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A: Y=3x-4

Q: 19. Evaluate Scx ds, where C is a. the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).…

A: Part (a)

Q: find a parametrization c(t) of the curve satisfying the given condition.  y = 3x − 4, c(3) = (2, 2)

A: To find the parametrization

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Q: find a parametrization c(t) of the curve satisfying the given condition. y = x2, c(0) = (3, 9)

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A: Given information:  The parametric equations are x(t)=−6t2−6t,y(t)=−4t3−6t2 over the interval .0≤t≤1…

Q: 10. A particle moves in the xy-plane so that the position of the particle is given by x(1) =1+cos t…

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Q: 3. A particle moving along a curve in the xy-plane has position (x(t1),y(t)), with x(1)= 2t +3sin t…

A: Velocity is equal to the first derivative of position vector   Let x =f1t and y =f2t then velocity…

Q: 1. The task is to identify the work done by B on a particle going from point (-1,1,-2) to (2, 4,4)…

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Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

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Q: Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes…

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Q: If the position vector (with its tail at origin) of a moving particle be t2i -2t + (t² +2t)k. then…

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Q: A bee with velocity vector r' (t) starts out at (2, 5, -2) at t = 0 and flies around for 1 seconds.…

A: We can answer first question as per the honor policy. Please resubmit other parts as well to know…

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Q: Find the equation of the plane that passes through the point (2, 1, 1) and is tangent to the surface…

A: We have to find the equation of the tangent plane.

Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (1, 1, 0) of…

A: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (1, 1, 0) of…

Q: Find a parametrization x = x(t), y = y(t), tE [0, 1] for the line segment from (-2, –5) to (–3, –7).…

A: To parameterize a  line segment with endpoint ( -2 , -5) and ( -3 , -7 )

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Q: Given the position vector 7 (t) = of a particle in space at time t. t

A: Given,           The position vector r→t = t+1, t, 1t of a particle in space at time t.

Q: Find the equation w=T(x,y,z) of the tangent hyperplane at p. F(x,y,z)=3x²-2y²+xz², p=(1,2,-1)

A: General equation for the tangent to the plane is expressed as:…

Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = &lt; -2, 5, 4&gt;     ---(1)  B(t) = &lt; 3/5 cos t , 3/5 sin t , 4/5 &gt;    =&gt; B(0)  =…

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Q: Find a parametrization for the ray (half line) with initial point (3,4) when t=0 and (0, - 1) when t…

A: Line equation.

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