QUESTION 3 Let r(t)=(1-t?,5t,2t3). r'(3). Find the z-component of the vector

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: The position of a particle moving in space at time t>=0 is r(t) = 2i + (4 sin t/ 2) j + (3 -…

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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: Q3): If A = 2i-j+ k, B = i + 2j - k and C = i + j - 2k, find unit vector orthogonal to A in plane of…

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Q: 6. A particle moves in the xy-plane in such a way that its velocity vector is (1+1, 1). If the…

A: Find the position vector

Q: QUESTION 2 The y-coordinate of the initial point of the vector v=-2i-9j whose terminal point is…

A: We will find the y coordinate as following.

Q: QUESTION 1 Let C be the oriented curve parameterized by r(t)= for 0sts2 (so C is actually an…

A: Given integral is

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x= 2+3t y…

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Q: 1) The domain of the vector position r(t) = 1+2 i+ sintj+ In(9- t²) k

A: We are entitled to solve only 1 question at a time so, I am providing you the solution of the first…

Q: If an object follows the path of the two-dimensional vector-valued function p(t)=(16−cos(t),…

A: Given p(t)=(16−cos(t), 0.6πt−0.15t2−3)

Q: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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Q: A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the…

A: Start from the origin, move p units to the right along the x axis and q units up along the y axis to…

Q: 5Let MH)=Hit2costj + (2shnt-3k a) Find unit tingent vector TH) of rtH)

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Q: QUESTION 10 Let r(t)=(1-t2, 5t, 2t3). Find the z-component of the vector r'(4).

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Q: 2t + 3 r(t) = -, In(t² + 2) t² +1' describes the position of a particle in the plane, for t> 0.…

A: We have to find the unitary tangent vector at t=2.

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: Question 2 Show that the divergence of x is à where r is the magnitude of the vector r and î…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Find a normal vector at point P. xy2 - 4x2 + y + 8x = 7, P(4, 3) Find a tangent vector at point P.

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Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

Q: Q3/A- Show that for any position vector r the binomai vector B is always orthogonal to the…

A: We have to solve given problems:

Q: Find the position vector for a particle with acceleration, initial velocity, and initia a(t) = (2t,…

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Q: Question 6 For the vector v whose initial point (-3, a) and terminal point(5,b). Also given b - a =…

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

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Q: ion 2. Find the domain of the vector function r(t) = (√5 – t², 1⁄2, et). t-

A: A  vector-valued function, also referred to as a vector function, is a mathematical function of one…

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

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Q: 4. A vector normal to the paraboloid z = (x² + y*)/2 is (a) (х, у.1). (b) (2x,2y,–1). (e) (-х,-у.1).

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Q: B) The vector v = (3cost)i + (3sint)j +t2k .gives the position of a moving body at time t. find 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: The vectorr(t) is the position vector of a particle at time t. Find the angle between the velocity…

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Q: An airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration…

A: Let r(t) be a position vector of a particle at time t. Then the velocity vector  v(t)=ddtr(t) Also…

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…

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

A: We have acceleration, initial velocity, and initial position, and if we integrate acceleration with…

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: Find the binormal vector for 7(t) = (3t, sint, cos t) А. ВО cost, sint V10 10 1 B(e) = (- 3 В. ВО)…

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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: 3x2 – 4y2 at which the vector 11. Find the points on the graph of z = (3, 2, 2) is normal to the…

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Q: 1. The position of a particle moving in the ry plane at time t units is given by the vector equation…

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Q: The graph of the vector functionr (t) = 2i +tj+tk is

A: 3d graph related problem.....

Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

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Q: Question 3 Determine which vector from the options below is in the plane: 1 I = S + tl 2 - TO Omo

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Q: 1. A certain velocity vector V has an X-component, V,, of 12 m/s, and a Y-component, V, of 9 m/s.…

A: To find the magnitude of the velocity vector V.

Q: Find the vectors T and N at the given point: r(t) = (cos t, sint, In sin t); (0, 1, 0).

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Q: Question 13 at t 1. Find the velocity, speed. and acceleration of the vector-valued function Kt) =…

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Q: Question 4 Find r'(t) given the following vector function. r(t) = 2/³i+34j+37²k O r'(t) =…

A: We have to find out derivative

Q: Find the tangent vector of r(t) = (t° , 3tª) at time t = 1. A) (3, 12) B) 15 C) (3, 7) D) 3t2 + 12t3

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Q: Question 4 is not smooth. Assume b=11. Find the value of a at which the plane curve traced out by…

A: The given vector function is r(t)=a25t3-t,t22+bt, where b=11