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The slope of the characteristic lines is $2/5$. This is derived from the direction vector (5,2), where the change in y is 2 and the change in x is 5, so $dy/dx = 2/5$.

Conditions: The direction vector is (5,2).; The characteristic lines are straight lines in the xy-plane.

The slope of the characteristic lines is $2/5$. This is derived from the direction vector (5,2), where the change in y is 2 and the change in x is 5, so $dy/dx = 2/5$.

Conditions: The direction vector is (5,2).; The characteristic lines are straight lines in the xy-plane.

The equation (5,2)·∇$u=0$ implies that the directional derivative of u in the direction of the vector (5,2) is zero. This means that the rate of change of u is zero when moving in that specific direction.

Conditions: The direction vector is (5,2).; ∇u is the gradient of u.

The equation (5,2)·∇$u=0$ implies that the directional derivative of u in the direction of the vector (5,2) is zero. This means that the rate of change of u is zero when moving in that specific direction.

Conditions: The direction vector is (5,2).; ∇u is the gradient of u.