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The gradient of the function ( f(x, y, z) = xi + yj + zk ) is given by the vector of its partial derivatives with respect to each variable.
Calculating the gradient:
[
nabla f = left( frac{partial f}{partial x}, frac{partial f}{partial y}, frac{partial f}{partial z} right) = (i, j, k) = (1, 1, 1)
]
So, the gradient of the vector field ( xi + yj + zk ) is:
[
nabla f = (1, 1, 1)
]
Answer: d
Explanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. In other words, the gradient of any
position vector is 3.