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:…
Read MoreVector 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…
Read MoreScalar triple Product Properties of Scalar triple Product: Example : Soln: = 1 ( 1 – 0 ) – 1 ( 0 – 1 ) + 0 ( 0 – 1 ) = 1 ( 1 ) -1 (- 1 ) + 0 = 1 + 1 = 2 Example : Soln: = 2 ( 4 + 2 ) – 1 (3 – 1 ) + 1 ( -6 – 4 ) = 2 ( 6 ) – 1 (2 ) + 1 ( – 10 ) = 12 –…
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