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

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

Find a vector in component form that is perpendicular to the line 3x 4y = 6.

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

Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes through the point (6, 1, −3). Find a parametrization for each of the lines. (Use a different variable for the two parameters.)

Find the scalar equation of the line through (3,-2) and perpendicular to the line r = (4,-3) + t(-5,1) .  Please answer.  Thank you

Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the components of a new point?

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.