A particle is located at the point (2, 7) on a metal surface whose temperature at a point (x, y) is T(x, y) = 16 - 2x² - 3y². Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y = E) 1

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Quizplus · Accepted Answer

First, we need to find the gradient vector of temperature (T) at point (2,7): ∇T = ⟨-2², -3²⟩ Then, we need to find the unit vector in the direction of maximum temperature increase: u = ⟨-2², -3²⟩ / ||⟨-2², -3²⟩|| = ⟨-2/13, -3/13⟩ Finally, we can use the point-slope form of a line to find the equation of the trajectory: y - 7 = (-3/2)(x - 2) Simplifying, we get: y = (-3/2)x + 10.5 Therefore, the correct answer is choice B.

A Particle Is Located at the Point (2, 7) on a Metal