The vector field V(r) = v(p) where p = √² + y², and is the unit vector of polar coordinate. √/z²+y² (a) Please calculate F=V x V. v(p) = p, F₂(x = 1, y = 1) =? (b) If V x V = 0, find v(p). (=?

Q: A. B. Let the position vecor be R(t) = (-t, 4 cos (2t), 4 sin(2t)). Compute the principal unit…

A:

Q: The directional derivative of x,y) - 16/x - 13y at the point (11,8) in the direction of the given…

A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

Q: The smooth vector-valued function P(t) satisfies P(2)= (-4, 8,-7), P′(2)= (0,-5,2), and P'(2)= (3,…

A:

Q: Express the following vector function in a component form. r(t)=t°j+(cos 2t)k

A: The vector function is given as , rt=t3j^+cos2tk^ express in component form.

Q: For the line that has the equation X1 + 2X2 = 10, will pass through: %3D O (5,4) (10,1) O (2,4) O…

A: Given that  The equation of a line is x1+2x2=10 To find a point that will pass through the given…

Q: (a) Find [F(t) • G(t)] (b) Given p(t) = 3VE , evaluate [p(t)F(t)] dt

A:

Q: COS 1,sin 2t) and R(0) = (1,0.–1). Let R be a vector function such that T(t) = (cos 2t, 2/2, Find An…

A: Given : T→=32cos2t , 12 , 32sin2t, R→0=1 , 0 , -1. To Find: The equation of the osculating plane,…

Q: Can you please help me solve this problem. I have attached the vector equation in the other image.

A: The first derivative of the vector function r(t) = (t sin(t), t², t cos(2t)) is given by r'(t). We…

Q: Find r(t) and the velocity vector v(t) given the acceleration vector a(t) = (8e¹, 14t, 16t + 8), the…

A:

Q: Which of the following vector-valued functions represent the same graph? (Select all that apply.)…

A:

Q: Find an equation of the plane that contains the curve with the given vector equation. r(t) = (2…

A:

Q: Let 7 (t) = (4t³ – 4, – 3e", – 3 sin( – 4t)) - Find the unit tangent vector T(t) at the point t = 0…

A:

Q: (a) Find the direction for which the directional derivative of the function f(x, y) = 9xy + 2y is a…

A: Formula for directional derivative Du→fP=∇f(P).u^=∇f(P)u^cosθ Du→fP to be maximum angle θmust be 0.…

Q: Question 1 Define the two vector valued functions of one variable u(t)= (-1/t, 2t, t²), v(t) := (t²,…

A: Let's find derivative of vector function.

Q: 3. Find an equation of the plane tangent to the Bohemian dome S described by the vector function…

A:

Q: iven belo

A: The value of derivative of vector R→t, R'→t=2e2t-4,6t2,1t-1  Integrating the derivative vector with…

Q: Evaluate the vector-vall function at each giver r(t) = cos(t)i + 3 sin(t)j (a) r(0) = (b) г(π/4)=…

A:

Q: Let 7(t) = (3 cos(t), 3 sin(t), 3t) and P = (3, 0,6). Consider the curve c parametrized by F(t).…

A: