Question

Suppose that over a certain region of space the electrical potential v is given by the equation v(x, y, z) = 5x² - 4xy - xyz. What is the electrical potential at a point (2, -3, 4)?

Answer 1

The electrical potential at the point (2, -3, 4) for the given potential function v(x, y, z) = 5x² - 4xy - xyz is 68 volts.

Step-by-step explanation:

To determine the electrical potential at a point (2, -3, 4) given the potential function v(x, y, z) = 5x² - 4xy - xyz, we simply substitute the coordinates of the point into the function:

v(2, -3, 4) = 5(2)² - 4(2)(-3) - (2)(-3)(4)

= 5(4) + 24 + 24

= 20 + 48

= 68 V

Therefore, the electrical potential at the point (2, -3, 4) is 68 volts.