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REV:Vectors in 2D & 3D
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Unit vector =
length =
Dot product =
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Directional Derivative.
Example3 Find the directional derivative of
. at (1,1) in the direction of
(A) the unit vector
(B) a unit vector in the direction of 3i+4j ….(C) a unit vector whose angle with the positive x-axis is
(D) The unit vector 0i+j
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Generalization of Partial Diff
In this section we will introduce a type of derivative, called a directional derivative.
Suppose that we wish to find the directional derivative of f at (x0,y0) in the direction of an arbitrary unit vector u = <a,b>
To do this we consider the surface S with equation z=f(x,y) And we let z0=f(x0,y0) then the point P(x0,y0,z0) lies on S.
The vertical plane that passes though P in the direction of u intersects S in a curve C.
The slope of the tangent line T to C at P is the directional derivative of f at (x0,y0) in the direction of u
See this link
See this
Directional Derivative.
Example5 Find the directional derivative of
. at (1,-1,2) in the direction of:222 4),,( zyxxyzyxF
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