Transcription of LECTURE 2: VECTOR MULTIPLICATION - SCALAR AND …
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LECTURE 2: VECTOR MULTIPLICATION - SCALAR AND …
LECTURE 2: VECTOR MULTIPLICATION - SCALAR AND VECTORPRODUCTSProf. N. HarnewUniversity of OxfordMT 20121 Outline: 2. VECTOR SCALAR Properties of SCALAR Angle between two VECTOR Properties of VECTOR VECTOR product of unit VECTOR product in Geometrical interpretation of VECTOR SCALAR ProductScalar (or dot) product |a|.|b|cos abcos (write shorthand|a|=a ).IScalar product is the magnitude ofamultiplied by the projection ifais perpendicular |a|2(since =0 )Hencea= ( ) Properties of SCALAR product (i) (ii) This leads (axi+ayj+azk).(bxi+byj+bzk)=axbx+ayby+az bz(this is a very useful relation)iii) : commutativea.(b+c) = + : distributive(iv) Ifc=a+bThenc2= (a+b).
Outline: 2. VECTOR MULTIPLICATION 2.1 Scalar Product 2.1.1 Properties of scalar product 2.1.2 Angle between two vectors 2.2 Vector Product 2.2.1 Properties of vector products 2.2.2 Vector product of unit vectors 2.2.3 Vector product in components 2.2.4 Geometrical interpretation of vector product 2.3 Examples 2
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