What is the projection of #<-7 , 3, -5 ># onto #< 4, -5, 1>#?

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Answer 1 · 2016-11-07T15:13:28

The projection #=〈-32/7,40/7,-8/7〉#

The projection of #vecb# onto #veca# is given by
#=(veca.vecb)/(∥veca∥*∥veca∥)veca#

The dot product is
#veca.vecb=〈-7,3,-5〉.〈4,-5,1〉=-28-15-5=-48#

The modulus of #veca# #=∥veca∥=∥〈4,-5,1〉∥=sqrt(16+25+1)=sqrt42#

The projection is #=-48/42〈4,-5,1〉=-8/7〈4,-5,1〉#