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## Vectors

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**a**a b Vectors C4 Scalar Product The scalar (or dot) product is a way of combining two vectors that results in a useful scalar value.**a**a b ? ? Vector Product Def. Vector Product The vector (or cross) product is a way of combining two vectors that results in a useful vector. Right-hand rule. Screwdriver undoing a screw.**Vector Product**There was an easy alternate way to find the scalar product, found by considering unit vectors. There must be an easy way to find the cross product too. Idea**Ex**? Vector Product Def. Vector Product (determinant form)**Vector Product**Ex Page 106 Exercise 5A**C**A A Res. B B O O Applications of Vector Products ?**Applications of Vector Products**Ex Page 110 Exercise 5B**Scalar Triple Product**Def. Scalar Triple Product**Scalar Triple Product**? The Volume of a Parallelopiped**Scalar Triple Product**? What is the volume of this tetrahedron?**Scalar Triple Product**Ex Page 113 Exercise 5C**b**r a Vector Equation of a Line C4 A line goes through point A and is parallel to a vector b • To get to any point on the line from the origin • Move from O to A • Move along the line some distance b R A O**R**b A r a O Def. Cross Product Equation of a Line Cross Product Equation of a Line Idea**Def.**Cartesian Equation of a (3D) Line Cartesian Equation of a Line Idea Page 113 Exercise 5D**Equation of a Plane**Idea A O**Equation of a Plane**Idea A R O**Def.**Cartesian Equation of a Plane Cartesian Equation of Plane Idea**Equation of a Plane**Ex Page 120 Exercise 5E**Equation of a Plane**Ex Page 128 Exercise 5F**Labels**M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise