Lecture 4-1

# Lecture 4-1 - Cross products mechanics Warmup Question:...

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Cross products: mechanics

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Warm up Question: two vectors span a parallelogram. What is the area of the parallelogram? What is a unit vector perpendicular to the parallelogram?
Warm up Example: how about the parallelogram spanned by the two vectors and in the ­plane? æ 4, 0 ç æ 3, 4 ç xy

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Warm up Example: how about the parallelogram spanned by the two vectors and in the ­plane? æ 4, 0 ç æ 3, 4 ç xy
Warm up Example: how about the parallelogram spanned by the two vectors and in the ­plane? æ 4, 0 ç æ 3, 4 ç xy The area is thus . 4 Ğ 4 = 16

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Magic on the way It turns out that there is a way to make a single vector encoding both the perpendicular direction and area of the parallelogram.
Magic on the way It turns out that there is a way to make a single vector encoding both the perpendicular direction and area of the parallelogram. Secret sauce: the cross product

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Definition The cross product of two vectors is the vector a = æ , , ç , b = æ , , ç a 1 a 2 a 3 b 1 b 2 b 3 a × b = æ J , J , J ç . a 2 b 3 a 3 b 2 a 3 b 1 a 1 b 3 a 1 b 2 a 2 b 1
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Lecture 4-1 - Cross products mechanics Warmup Question:...

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