The force in an electrostatic field given by f(x, y, z) = 2x^2 + 4y^2 + 9z^2 has the direction of the gradient. Find ∇f and its value at P : (−1; 2;−4).
The gradient is given by,
∇f = (δf/δx).i + (δf/δy).j + (δf/δz).k
gradient = (4x).i + (8y).j + (18z).k
At P(-1, 2, -4), Gradient f = (4x).i + (8y).j + (18z).k x = -1, y = 2, z = -4
Gradient f = (-4).i + (16).j + (-72).k
Gradient f = -4.i + 16.j – 72.k
Had some problems entering info. Couldn't use the Grad operator. The text after it kept disappearing!!