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**Unformatted text preview: **Let u = ( u 1 , u 2 , ..., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u v is defined to be: u v = u 1 v 1 + u 2 v 2 + . . . + u n v n Sec 5.1 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 1 Let u = ( u 1 , u 2 , ..., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u v is defined to be: u v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. 5.1.1 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 2 Let u = ( u 1 , u 2 , ..., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u v is defined to be: u v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. u v = 5 x 3 + 3 x 1 + 1 x (-1) = 15 + 3 - 1 = 17 5.1.2 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 3 Let u = ( u 1 , u 2 , . . ., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u v is defined to be: u v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. u v = 5 x 3 + 3 x 1 + 1 x (-1) = 15 + 3 - 1 = 17 u v = 2 x (-4) + 3 x (-6) + (-1) x 2 + 4 x 7 = - 8 - 18 - 2 + 28 = 0 5.1.3 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 4 Let u = ( u 1 , u 2 , . . ., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u v is defined to be: u v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. u v = 5 x 3 + 3 x 1 + 1 x (-1) = 15 + 3 - 1 = 17 u v = 2 x (-4) + 3 x (-6) + (-1) x 2 + 4 x 7 = - 8 - 18 - 2 + 28 = 0 u u = 5 x 5 + 3 x 4 + 1 x 1 = 5 2 + 3 2 + 1 2 = 25 + 9 + 1 = 35 * 5.1.4 Saturday, February 06, 2010 11:13 PM Section5dot1 Page 5 Let u = ( u 1 , u 2 , . . ., u n ) and v = ( v 1 , v 2 , ..., v n ) be vectors in R n . The dot product. u v is defined to be: u v = u 1 v 1 + u 2 v 2 + . . . + u n v n Also called the scalar product or the inner product of vectors. u v = 5 x 3 + 3 x 1 + 1 x (-1) = 15 + 3 - 1 = 17 u v = 2 x (-4) + 3 x (-6) + (-1) x 2 + 4 x 7 = - 8 - 18 - 2 + 28 = 0 u u = 5 x 5 + 3 x 4 + 1 x 1 = 5 2 + 3 2 + 1 2 = 25 + 9 + 1 = 35 * | u | = u 1 2 + u 2 2 + u 3 2 = 5 2 + 3 2 + 1 2 = 35...

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