MA10236B 1

MA10236B 1

1. 1.1 Introduction to vector algebra

   • D1.1 A vector is a directed line segment.
   • D1.2 The length of PQ is the distance between P and Q, this is denoted ||PQ||. We often say it is the norm of ||PQ|| is the norm of PQ.
     • D1.3 If P=Q, then the vector is called the zero vector.
   • D1.5 Two vectors PQ and RS are said to be parallel (collinear) if they lie on parallel straight lines L1 and L2. The zero vector is regarded to being parallel to any vector.
   • D1.6 Two vectors are said to equal (PQ=RS) if they are collinear, have the same magnitude and have the same direction.

2. 1.2 Basic operations with vectors

   • D1.7 c=a+b
   • Properties of vectors
     • P1 a+b=b+a
     • P2 (a+b)+c=a+(b+c)
     • P3 a+0=a=0+a
     • P4 a+(-a)=0
     • P5

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