This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: a R n has length one, that is  a  = 1 . Denition 1.6. The standard basis in R 3 is denoted by i , j , k is given by i = (1 , , 0) , j = (0 , 1 , 0) , k = (0 , , 1) ADD PICTURE Remark 1.2. i , j and k are unit vectors. Example 1.1. i + j = j + i . ADD PICTURE Lemma 1.1. Any vector in R 3 can be decomposed into a sum of scalar coecients multiplying the three standard basis vectors. Proof. Algebraic: Let a = ( a 1 ,a 2 ,a 3 ) be a vector in R n . Then a = a 1 e 1 + a 2 e 2 + a 3 e 3 . Geometric:: ADD PICTURE Example 1.2. If a = 2 i + 3 j and b =j + 2 k sketch 2 a2 b . Remark 1.3. One can also use vectors to describe lines and planes. As an example, the xy plane is the set of all points i + j where , R . Simliarly the yz plane is the set of all points j + k where , R . 2...
View Full
Document
 Winter '08
 JackWaddell
 Vector Calculus, Vectors

Click to edit the document details