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# notes001 (8) - The Dot Product Outline of Hass Weir Thomas...

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e Dot Product The Dot Product Outline of Hass, Weir, Thomas – Section 9.3

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efinition Definition Let u u 1 , u 2 , u 3 and v v 1 , v 2 , v 3 be vectors. The dot product, u v , is defined to be u v u 1 v 1 u 2 v 2 u 3 v 3 . xample Example Let u 2, 3, 1 and v 1, 5, 3 . ompute Compute u v .
Basic Algebraic Properties of the Dot Product If u , v and w are any vectors and k is a scalar, then y , 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 | u | 2 5) u 0 0 . By using the above properties, we also obtain 2 2 2 6) | u v | | u | 2 u v | v | 7) | u v | 2 | u | 2 2 u v | v | 2

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The Law of Cosines For any triangle (as pictured), we have c 2 a 2 b 2 2 ab cos C b 2 a 2 c 2 2 ac cos B a 2 b 2 c 2 2 bc cos A . Prooftobeg
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notes001 (8) - The Dot Product Outline of Hass Weir Thomas...

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