3.7 - Section 3.7 Cross Products In this section, we'll be...

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Section 3.7 Cross Products In this section, we’ll be looking for a vector that is orthogonal to two given vectors. There are an infinite number of answers! One specific one is called the cross product. THE CROSS PRODUCT OF TWO THREE-DIMENSIONAL VECTORS LET u = 1 2 3 u u u    AND v = 1 2 3 v v v .
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THE CROSS PRODUCT OF u AND v IS THE VECTOR: u × v = i j k u 1 u 2 u 3 v 1 v 2 v 3 = . (EXPANDING ALONG ROW 1) i u 2 u 3 v 2 v 3 + j(-1) u 1 u 3 v 1 v 3 + k u 1 u 2 v 1 v 2 = (u 2 v 3 -u 3 v 2 )i - (u 1 v 3 - u 3 v 1 )j + (u 1 v 2 -u 2 v 1 )k
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= u 2 v 3 u 3 v 2 u 3 v 1 u 1 v 3 u 1 v 2 u 2 v 1 . THE VECTOR u × v IS ORTHOGONAL TO BOTH u AND v. Example: Find u X v for 10 2 a n d 3 31 uv   ==  u 2 v 3 u 3 v 2 u 3 v 1 u 1 v 3 u 1 v 2 u 2 v 1 Just plug in the values.
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2( 1) 3(3) 3(0) 1( 1) 1(3) 2(0) −−
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This note was uploaded on 10/16/2009 for the course MATH 1114 at Virginia Tech.

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3.7 - Section 3.7 Cross Products In this section, we'll be...

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