Science:Math Exam Resources/Courses/MATH200/December 2013/Question 01 (e)
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Question 01 (e) 

Suppose it is known that the direction of the fastest increase of the function at the origin is given by the vector . Find a unit vector that is tangent to the level curve of that passes through the origin. 
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Hint 

Science:Math Exam Resources/Courses/MATH200/December 2013/Question 01 (e)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The direction of the fastest increase of a function is in the direction of the gradient of the function. The gradient of the function is orthogonal to the level curves of the function, therefore, we want to look for a vector that whose dot product with is . Such a vector is Converting this into a unit vector, we get
