Find proivu and projuv Use the Euclidean inner product u 2 1

Find proivu and projuv. Use the Euclidean inner product u (2, -1, 1), VE (2, -1, -1) (a) proju (b) projuv

Solution

U= 2 -1 1 V= 2 -1 -1 PRODUCT 4 1 -1 U.V= 4 U= 2 -1 1 U= 2 -1 1 PRODUCT 4 1 1 U.U= 6 |U|=[U.U]^0.5= 2.44949 V= 2 -1 -1 V= 2 -1 -1 PRODUCT 4 1 1 V.V= 6 |V|=[V.V]^0.5= 2.44949 VECTOR PROJECTION OF U ON V = [(U.V)/(|V|)]*[V] VECTOR PROJECTION OF U ON V = ( 4 /2.44949)*[V] VECTOR PROJECTION OF U ON V =   3.265986 -1.63299 -1.632993162