Question

Suppose that over a certain region of space the electrical potential v is given by the following equation: v(x, y, z) = 2x² - 3xy - xyz. What is the value of v at the point (2, -1, 3)?

Answer 1

The value of the electrical potential at the point (2, -1, 3) for the given potential function v(x, y, z) = 2x² - 3xy - xyz is 20 volts.

Step-by-step explanation:

The student's question relates to finding the electrical potential at a specific point in space, given a potential function v(x, y, z) = 2x² - 3xy - xyz. To find the value of v at the point (2, -1, 3), we simply substitute these values into the equation:

v(2, -1, 3) = 2(2)² - 3(2)(-1) - (2)(-1)(3)

Calculating this, we get:

v(2, -1, 3) = 2(4) + 6 + 6

v(2, -1, 3) = 8 + 6 + 6

v(2, -1, 3) = 20 V

Therefore, the value of the electrical potential v at the point (2, -1, 3) is 20 volts (V).