What is the projection of #< -2, 4, 7># onto #< -5, 9, -5>#?

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Answer 1 · 2018-07-22T17:45:32

The projection is #=(11)/131*<-5,9,-5>#

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

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

Here,

#veca= <-5,9,-5>#

#vecb = <-2,4,7>#

Therefore,

The dot product is

#veca.vecb=<-5,9,-5> . <-2,4,7> =10+36-35=11#

The modulus of #veca# is

#|veca| = |<-5,9,-5>| = sqrt(25+81+25)= sqrt131#

Therefore

#proj_(veca)vecb=(11)/131*<-5,9,-5>#