How to find direction from gradient?

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To determine the direction a shark should swim to find its prey based on the gradient <12,-20,5>, it is essential to understand that the gradient indicates the direction of steepest ascent in the context of the function f(x,y,z). The discussion raises confusion about whether the answer should be the gradient itself or its unit vector. It is suggested that the unit vector may be the desired answer, as it represents the direction without magnitude. Clarification on the question's intent is needed, but the gradient provides a clear directional cue for the shark. Understanding the gradient's role is crucial for solving similar problems in vector calculus.
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Homework Statement


if f(x,y,z) indicates electrical charge in the water at position(x,y,z) and
the gradient is <12,-20,5>, in which direction should the shark swim to find its prey?


Homework Equations





The Attempt at a Solution


is the answer in the direction of <12,-20,5>
im little confused when gradient is given and how to find direction? do i find unit vector of gradient or something?
 
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Yeah, the question is not very clear. I would guess that you have the right answer. Or maybe they want the unit vector, as you say.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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