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Lecture 4-2

# Lecture 4-2 - Cross products geometry Giventwovectors and...

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Cross products: geometry

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Sweet Sweet Theorem for Given two vectors and with angle the vector is to both and ; the list satisfies the right­hand rule; we have ; equals the area of the parallelogram spanned by and . × a b ' a × b þ a b a , b , a × b | a × b | = | a || b | sin( ' ) | a × b | a b
Sweet Sweet Theorem for Given two vectors and with angle the vector is to both and ; the list satisfies the right­hand rule; we have ; equals the area of the parallelogram spanned by and . Ties the cross product to area and orientation. × a b ' a × b þ a b a , b , a × b | a × b | = | a || b | sin( ' ) | a × b | a b

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Do one Example: find the area of the parallelogram spanned by and Compute the cross product! Can you predict the direction of the cross product vector without calculating anything? Can you predict the magnitude of the cross product without calculating anything? e 4, 0, 0 f e 3, 4, 0 f
I did it Example: find the area of the parallelogram spanned by and Compute the cross product!

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Lecture 4-2 - Cross products geometry Giventwovectors and...

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