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Properties (III):( ) ,( )| | = | || | equals to the area ofthe parallelogram determined by and . The Right Hand Rule: If the fingers of your right hand curl in the direction of a rotation from to , then your thumb points in the direction of .
Properties (IV): ·( )=( )· ·( ) is called the scalar triple product of , , . ·( )=The volume of the parallelepipeddetermined by the vectors , , equals | ·( )|.
Ex: Find an equation of the plane throughthe point ( , , ) with normal vector , ,Ex: Find an equation of the plane that passesthrough ( , , ), ( , , ) and ( , , ).Ex: Find the point at which the line withparametric equations = + , = + , =intersects the plane + = .Ex: Find a equation for the line ofintersection of two planes = , + = .