MATH 101 Lecture Notes - Lecture 3: Dot Product
5 Sep 2016
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Math 212 section 11. 3 the dot product of two vectors. You have studied two operations with vectors vector addition and multiplication by a scalar each of which yields another vector. In this section you will study a third vector operation, called the dot product. This product yields a scalar, rather than a vector. Find the following: (cid:1873) , (cid:1874) , (cid:4666) (cid:1873) , (cid:1874) ) (cid:1875) , (cid:1873) , (cid:884) (cid:1874) , (cid:1875) (cid:2870) The angle between two nonzero vectors is the angle , 0 , between their respective standard position vectors as shown in the figure. If the angle between two vectors is known, rewriting theorem 11. 5 in the form produces an alternative way to calculate the dot product. From this form, you can see that because || (cid:1873) || and || (cid:1874) || are always positive, (cid:1873) : (cid:1874) and cos will always have the same sign. The possible orientation of the two vectors is below.
