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# Lecture 2 EMT - Vector Product • The cross(or vector...

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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 right-hand rule) • The product of cross product is a vector N AB a B A B A θ sin | || | = × a N a N Right-hand 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 θ AB = |A||a B | cos θ AB or A B = A·a 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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Lecture 2 EMT - Vector Product • The cross(or vector...

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