B = < 4xy² 2³, 4x²yz, - y² z4 - 2x² z² > ①check that div (B) = 0 ②Find a vector potential for B.

A force field is given by the equation. A particle is moved from (1,0,0) to (1,1,1) along a straight line. Calculate the work done by the force field on the particle.

B = ① check that div(B) = 0 ②Find a vector potential for B.

find the derivitive, r'(t), of the vector function.  r(t)=a+3tb+t^7c

Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

Suppose that over a certain region of space the electrical potential V is given by the following equation. V(х, у, 2) %3 4x2 - Зху + хуz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i +j- k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?

What is the velocity​ vector?

Find the velocity vector v(t), given the acceleration vector a(t) = (3e¹, 7, 10t +9) and the initial velocity v(0) = (8,-5,3). (Use symbolic notation and fractions where needed. Give your answer in the vector form.) v(t) = 2(e' - 2)i + (3t-2)j + (3r² +9r+2)k Incorrect

If r(t) = acoswt+bsinwt, where a and b are constant vector, show that  r(t)xr'(t)=wa x b

6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2, 16/3). 3 y =