B = < 4xy²z³, 4x²yz, -y²z4-2x²z²> ① check that div(B) = 0 ②Find a vector potential for B.

What is the velocity​ vector?

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

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?

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

Find a unit vector parallel to the line y = 7x - 3. Use the scalar product to find the angle between the lines y = 7x - 3 and y = 2x + 7.

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

If ū = (, 2), find a vector i that is perpendicular to ū.

A PARTICLE MOVES WITH A SPEED OF 2 m/s IN THE DIRECTION OF THE VECTOR a=(5,-3,2) determine the x, y, and z components of the velocity vector