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To compute the divergence of the vector field F = xi + yj + zk, we use the formula for divergence in three dimensions, which is given by:
∇ · F = ∂(F₁)/∂x + ∂(F₂)/∂y + ∂(F₃)/∂z
where F = (F₁, F₂, F₃) = (x, y, z).
Calculating the partial derivatives:
1. ∂(F₁)/∂x = ∂(x)/∂x = 1
2. ∂(F₂)/∂y = ∂(y)/∂y = 1
3. ∂(F₃)/∂z = ∂(z)/∂z = 1
Now, we can sum these results:
∇ · F = 1 + 1 + 1 = 3
Thus, the divergence of the vector field xi + yj + zk is 3.
Answer: d
Explanation: The vector given is a position vector. The divergence of any position vector is always 3.