Direction Angles and Direction CosinesThe direction angles of a nonzero vector arethe angles that it makes with the positive x-,y-, and z-axes. · · = = = = | || | | | | || | | | · = = | || | | | + + = =| | , ,
Projections:The scalar projection of onto (also calledthe component of onto ) is defined to be · =| | = calar! | | sig ne d sThe projection of onto is defined to be · · = = ve ctor! | | | | | |
12.4 The Cross Product The cross product of = , , and = , , is given by = , , = = + It can only be defined for 3D vectors.
Properties (III):( ) ,( )| | = | || | equals to the area ofthe parallelogram determined by and .
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 .