notes001 (41)

notes001 (41) - v j 2 = ( u v ) & ( u v ) by...

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August 25, 2010 NAME____________________________ Recall the following properties of dot products: If u and v are any vectors and k is any scalar, then 1) u v = v u 2) ( k u ) v = u ( k v ) = k ( u v ) 3) u ( v + w ) = u v + u w 4) u u = j u j 2 5) u & 0 = 0 . Use the above properties (whichever are needed) to prove that if u and v are any vectors, then j u ± v j 2 = j u j 2 ± 2 u v + j v j 2 . each line of the proof indicating which of the above ±ve properties you are using in that step of the proof. Remember to write ² = ³where needed! Proof: j u ±
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Unformatted text preview: v j 2 = ( u v ) & ( u v ) by property 4 = ( u + ( v )) & ( u + ( v )) by denition of u v = ( u + ( v )) & u + ( u + ( v )) & ( v ) by property 3 = u & ( u + ( v )) + ( v ) & ( u + ( v )) by property 1 = u & u + u & ( v ) + ( v ) & u + ( v ) & ( v ) by property 3 = u & u u & v v & u + v & v by property 2 = u & u u & v u & v + v & v by property 1 = j u j 2 2 u & v + j v j 2 by property 4. This completes the proof. 1...
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This note was uploaded on 02/05/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

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