Question

Find the gradient of the function given by, x^2 + y^2 + z^2 at (1,1,1)

(a) i + j + k

(b) 2i + 2j + 2k

(c) 2xi + 2yj + 2zk

(d) 4xi + 2yj + 4zk

I had been asked this question during an interview.

My question comes from Gradient topic in portion Vector Calculus of Electromagnetic Theory

Answer 1

The correct answer is (b) 2i + 2j + 2k

To explain: Grad(x^2+y^2+z^2) = 2xi + 2yj + 2zk. Put x=1, y=1, z=1, the gradient will be 2i + 2j + 2k.