What direction should one move from point (2,3) to increase 4x^2y most rapidly? Present answer as a vector of length 1.
I have found the answer (48,16) but I do not know how to present the answer of length 1.
I know the solution is (1/(10)^0.5, 3/(10)^0.5) but I would like to know HOW to get that.
I have found the answer (48,16) but I do not know how to present the answer of length 1.
I know the solution is (1/(10)^0.5, 3/(10)^0.5) but I would like to know HOW to get that.
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Did you mean (16,48)?
A normalized vector is the vector in the same direction, but with unit length.
So to normalize a (non-zero) vector, a, first find its length, by calculating √(a.a). (Take the scalar (or dot) product of the vector with itself.)
Then divide each of the vector's components by the length.
In this case, it will be easier if we first divide each component by 16, getting (1,3).
(Since (1,3) is in the same direction as (16,48), it will normalize to the same vector.)
Length = √(1² + 3²) = √10.
So the normalized vector is (1/√10, 3/√10).
A normalized vector is the vector in the same direction, but with unit length.
So to normalize a (non-zero) vector, a, first find its length, by calculating √(a.a). (Take the scalar (or dot) product of the vector with itself.)
Then divide each of the vector's components by the length.
In this case, it will be easier if we first divide each component by 16, getting (1,3).
(Since (1,3) is in the same direction as (16,48), it will normalize to the same vector.)
Length = √(1² + 3²) = √10.
So the normalized vector is (1/√10, 3/√10).
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Glad to help.
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