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- The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = ti + (-t2 + 9)j (1, 8) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) s(t) = a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. v(1) = a(1)Evaluate the vector-valued function at each given value of t. (If you need to use At, enter Deltat.) r(t) = i - (t - 4)j (a) r(4) = 8 (b) r(0) (c) r(s+ 4) = (ar - 4at)i- 2aj (d) r(2 + At) - r(2) =At time t=0, a particle is located at the point (3,9,4). It travels in a straight line to the point (7,8,6), has speed 6 at (3,9,4) and constant acceleration 4i-j+2k. Find an equation for the position vector r(t) of the particle at time t -O+¹+* The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.)
- Write the vector equation of the line through (9,-1) and perpendicular to (x,y) = (1,-2) + t(6,-7)Find the linearization L(x,y) of the function at each point. f(x, y) = x2 + y2 + 1 a) (1,2) b) (2,4)Find the derivative of the vector function r(t) = ta x (b + tc), where a = (4,-1, 5), b = (-3,-3,-1), and c = (1,2, 2). r'(t) = ( 16+16t %3D 11+14t -15-18t
- Please solve (b) by finding a vector valued function f(t)=(x(t), y(t)) whose image set is the one givenYou are given the derivative of a vector function r in the component form is -(e,3e",-2t , dt ,3e",-2t). You are also given that r(0) = 21-j+k. r(0) = 2i -j+k J Determine the vector function r (t) in the form r(t)= (x(t),y(t), z(t)} An efficient notation for the vector equation of a straight line in 3D(or 2D) is given by ((t)- a+ bt where t is any real number, a is the position vector from the origin to a point on the line and b b) Write the vector equation of the tangent line to the curve C generated by r(t) at the point (2, -1, 1) using the above form aFind the domain of the vector function r(t)= <e-t , (t-5)1/2 , (7-t)1/2.
- The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = t'i + tj (4, 2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. v(2) = a(2) =The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = ti + (-t2 + 8)j (1, 7) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. v(1) = a(1)