What is the projection of #< 6 , -6 ,3 ># onto #< 4, 9, 1>#?

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Answer 1 · 2017-01-21T11:20:12

The vector projection is #=-27/98<4,9,1>#
The scalar projection is #=-27/sqrt98#

The vector projection of #vecb# onto #veca# is

#=(veca.vecb)/(|veca|^2)*veca#

The dot product is

#veca.vecb=<6,-6,3>.<4,9,1>=24-54+3=-27#

The modulus is

#|veca|=|<4,9,1>|=sqrt(16+81+1)=sqrt98#

The vector projection is #=-27/98<4,9,1>#

The scalar projection is

#=veca.vecb/|veca|=-27/sqrt98#