380. Find the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions. a) 0 b) 3 c) -3 d) 1
380. Find the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions. a) 0 b) 3 c) -3 d) 1
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Answer: b
Explanation: The position vector in Cartesian system is given by R = x i + y j + z k.
Div(R) = 1 + 1 + 1 = 3. By divergence theorem, ∫∫∫3.dV, where V is a cube with x = 0->1,
y = 0->1 and z = 0->1. On integrating, we get 3 units.