Question

The force in an electrostatic fi eld 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).

Answer 1

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!!

Comments

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