Rog_Sec_12_3

Rog_Sec_12_3 - (7/24/10) Math 20C. Lecture Examples....

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Unformatted text preview: (7/24/10) Math 20C. Lecture Examples. Section 12.3. The dot product and angles between vectors Definition 1 The dot product of vectors v = ( a 1 , b 1 ) and w = ( a 2 , b 2 ) in a coordinate plane is the number v w = a 1 a 2 + b 1 b 2 . If v = ( a 1 , b 1 , c 1 ) and w = ( a 2 , b 2 , c 2 ) are in xyz-space, then v w = a 1 a 2 + b 1 b 2 + c 1 c 2 . Example 1 Calculate v w for v = ( 6 , 2 ) and w = ( 4 , 3 ) . Answer: v w = 18. Example 2 What is v w for v = ( 6 , 2 , 3 ) and w = ( 4 , 3 , 6 ) . Answer: v w = 0 The dot product satisfies the following rules for any vectors u , v , and w and any number : v w = w v ( v ) w ) = v ( w ) = ( v w ) ( v + w ) u = v u + w u v v = | v | 2 The dot product is useful because of the next theorem. Theorem 1 If neither v nor w is the zero vector, then v w = | v || w | cos (1) where is an angle between v and w ....
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This note was uploaded on 08/31/2011 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

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Rog_Sec_12_3 - (7/24/10) Math 20C. Lecture Examples....

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