MATH1002 Lecture Notes - Lecture 7: Dot Product, Unit Vector, Cross Product
20 Aug 2018
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Document Summary
Normalisinga vector is what we call finding a unit vector with the same direction. Done by dividing a vector by its own length ||w w. The dot product can be used to find the angle between two vectors in standard position. We can use the dot product in conjunction with the cosine rule to determine the angle between nonzero vectors u and v. Cos = || u u|| ||v v dimension. || this is the formula for the angle between two vectors in any. Interesting note, the cauchy-schwarz inequality implies that || from 0 to 1, just like the cosine function. u v u|| ||v. If |u v| = ||u|| ||v|| then u and v are parallel (i. e. there exists a csuch that u = cv) Given two nonzero vectors in 3d space, we can define the vector v x w satisfying. V x w is orthogonal to both v and w.
