Question 4 Find r'(t) given the following vector function. r(t) = 2/³i+34j+37²k O r'(t) = 6t²i+12t³j+6tk O r'(t) = 6t²i+3t³j+3tk ○ r'(t) = 2t²i+3ť³j+ 3tk O r'(t) = 2t²i+3tj+3t³k r'(t) = 6t³i+12tªj+ 6t²k Question 5

Q: Compute the work done by the force 7 = (sin(x + y), xy, x²z) in moving an object along the…

A: Given force The object is moving along the straight line and from

Q: ent of acceleration and the principal ovided.

A:

Q: 8) Find a unit vector in the direction that f(x, y, z)=2x² +6xz²-yz³ increases most rapidly at the…

A: Given: A function fx , y , z=2x2+6xz2-yz3. To Find: Unit vector in the direction of the given…

Q: 42. Two boats B, and B2 are moving with velocities (4i – 3j + 7k) ms' and (2i + 3j + 4k) ms…

A: Velocities (4i-3j+7k) and (2i+3j+4k)

Q: b) Find the unit tangent vector of 7(t) = (t? – 1)î + t²j at t = 2.

A: We have to find the unit tangent vector.

Q: 2² Find wheref=x² + In(x²). dx² (*) Ⓒ*) O (*+)

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: The velocity of an object is given by V(t) = ti + e'j + te'k. Find the position function of the…

A:

Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

Q: Find r'(t), r(t,), and r'(t,) for the given value of to- r(t) = (5 + t)i + t°j, to = 1 r'(t) = r(t,)…

A: To find r'(t) and to sketch the curve represented by a vector-valued function and sketch the…

Q: Let x' = [4, 2, 1] and y' = [-1, 3, 0]. (a) Find 2x+y. (b) Find x'y. (c) Find the length of x, Lx.…

A:

Q: How do I find a vector b where, ||b|| = 9 direction =

A:

Q: What is the magnitude of the vector v with initial point P = (-4, 3) and terminat piont Q = (2, -5)…

A: A detailed solution is given below

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A:

Q: At time t=0 a particle at the origin of an x⁢y⁢z-coordinate system has a velocity vector of…

A: Using the basic general velocity formula, we get the velocity vector of the particle at time t to be…

Q: (3) This problem will walk you through the steps of finding a directional derivative through the…

A:

Q: In R, evaluate the alternating 2-form 5 = -3· dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: Given that, ξ=-3.dx∧dy on (a,b) Where a=(4,2,12),b=(-7,-4,8) The objective is to show that ξ(a,b).

Q: Given the vector-valued function

A: