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Unformatted text preview: Vector Product The cross (or vector) product of two vectors A and B, written as is defined as where a unit vector perpendicular to the plane that contains the two vectors. The direction of is taken as the direction of the right thumb (using righthand rule) The product of cross product is a vector N AB a B A B A sin    = a N a N Righthand Rule A direct application of vector product is in determining the projection (or component) of a vector in a given direction. The projection can be scalar or vector. Given a vector A , we define the scalar component of A along vector B as A B = A cos AB = Aa B  cos AB or A B = Aa B Components of a vector Dot product If and then which is obtained by multiplying A and B component by component. It follows that modulus of a vector is z z y y x x B A B A B A B A + + = ) , , ( z y x B B B B = ) , , ( z y x A A A A = 2 2 2   z y x A A A A A A + + = = Cross Product If A =(A x , A y , A z ), B =(B x , B y , B z ) then z y x y x y x z x z x z y z y z y x z y x z y x a B B A A a B B A A a B B A A B B B A A A a a a B A + + = = z x y y x y z x x z x y z z y a B A B A a B A B A a B A B A ) ( ) ( ) ( + + = Cross Product Cross product of the unit vectors yield: y a z x z y z y x a a a a a a a a a = = = Example 1...
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This note was uploaded on 02/18/2010 for the course EEE EEE 261 taught by Professor Sirimranawan during the Fall '10 term at COMSATS Institute Of Information Technology.
 Fall '10
 SirimranAwan

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