APPLICATION OF VECTOR DIFFERENTIATION

is a vector function, defined and differentiable at each point (x, y, z)in a certain region of space [i.e., A defines a vector field], then the divergence of  (abbreviated as ‘Div ‘) is defined as,  Basic properties of Divergence: If A, B are vector functions and ‘f’ is a scalar function, then Example: Soln: =   yz  + 3×2 ( 1 )  + ( 0 – y3 ) =  yz  + 3×2 – y3 Example: Soln: At ( 1, -1, 2) =    -2  – 4  – 1 =   -7 Example: Soln:…

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VECTOR DIFFERENTIATION

Vector point function and Vector field: Let P be any point in a region ‘D’ of space.  Let r be the position vector of P.  If there exists a vector function F corresponding to each P,  then such a function F is called a vector function and the region D is called a vector field. Example:  consider the vector function Let P be a point whose position vector is At P , the value of F is obtained by putting x = 2, Y = I, z = 3 in…

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