. Consider the force vector F = x²a,-xza, -y²a,. Calculate the work done in moving an object from point a to b along the path shown in Figure P1.36. (1,0,0) X Z (0,0,1) a (1,1,1) b (0,1,0) Figure P1.36 Contour of integra- tion of F.

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

A:

Q: 3. Calculate the directional derivative of the function f : R³ → R, defined by f(x, y, z) = y²+xz at…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find r'(t), r(t), and r'(to) for the given value of to r(t) = (1+t)i + ³j, to = 1 (No Response)…

A: We have to find the values of r't, rt0, r't0 where rt=1+ti^+t3j^, t0=1 and sketch the curve…

Q: QI-A) Fnd the position, vekocity and the speed of the vector function ( r(t) ) that given bekow at…

A: Given vector function is r(t)→=t2i-t3j To find the position, velocity and the speed of the vector…

Q: Find a unit vector u that is normal to the level curve of f(x, y) = 5x²y through P = (x, y) = (1,-4)…

A:

Q: Find the directional derivative of the scalar field = xy + 4xz at the point (2, -2, 4) along the…

A:

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: 1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a…

A:

Q: Find r'(t), r(t), and r'(t) for the given value of to. Then sketch the space curve represented by…

A:

Q: Consider the initial value problem [¼¼ = x³(y − n)² + eª sin(y); |y(0) = π. Find the solution of…

A:

Q: 1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction…

A: Step 1:

Q: Consider the function f(x,y) = ex cos y + e³ sinx and the points P(1,0) and Q(-3,3). Find Duf at the…

A: The given function is fx,y=excosy+eysinx and the points are P(1,0), Q(-3,3). The objective is to…

Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x,y,z)…

A:

Q: Show that the vector-valued function shown below describes the function of a particle moving in a…

A: Part - 1 : Given vector-valued function is                                      rt = 5i +5j +3k +…

Q: nd the increase rate of the scalar V at point P from origin to the point P(12 , 1,11 here V=…

A: As gradient of a scalar function gives the magnitude and direction of rate of change.

Q: Let F(x,y, z) = rye" – 2² Jī and P(1,0, –1).

A: Given Fx,y,z=xyey-z2x and P1,0,-1Vector u=⟨2,-3,6⟩

Q: The work done by the vector field F(x, y) = (-y², ²) along the arc of the parabola y = 2x² - 4x + 2…

A: According to question,Given Vector field,Fx, = -y2,x2Equation of pparabola,y = 2x2-4x+2

Q: 1) Sketch the vector field F. (i) F(r, y) = (ii) F(r,y, 2) = i

A:

Q: 2. See the following problem: Justify all solutions (give English explanations as you answe y' =…

A:

Q: Find a vector parametrization of the line through P = (0, -3, -2) in the direction V = (6, 4, 1)…

A: Step 1:   Step 2: Step 3: Step 4:

Q: Let f(x,y)=y2 +sin(y+T)+x +cos(xe). At the point (TT,0) compute the unit vector in the direction of…

A: We have to find the unit vector in the direction of the maximum increase of the function f. This…