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okay letamp;#39;s say you have a bunch of vectors like this and the question is which ones are perpendicular which ones are parallel uh which ones have angle less than pi over two between them angle more than pi over two so how do we do these questions well itamp;#39;s about a bunch of dot products so the important thing that you have to know is that if you have two vectors letamp;#39;s say u and v and if you compute their dot products itamp;#39;s zero that means that the two vectors are perpendicular another thing that you have to know that is that when two vectors are parallel that means uh one vector is like that and the other vector is in the same direction uh and the only difference is this thereamp;#39;s some multiple between them thatamp;#39;s called parallel and by the way even if they are exactly the opposite thatamp;#39;s still called parallel so uh so for parallel what you need is that two vectors are just multiples of one another so thereamp;#39;s some value k where
