What is the projection of #<3 ,-4, 7 ># onto #< -1 , 9,-2 >#?

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Answer 1 · 2016-12-22T09:28:19

The answer is #=-53/86〈-1,9,-2〉#

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

#=(veca-vecb)/(∣veca∣^2)*veca#

The dot product is

#veca.vecb=〈3,-4,7〉.〈-1,9,-2〉=(-3-36-14)=-53#

The modulus of #veca# is #=∣〈-1,9,-2〉∣=sqrt(1+81+4)=sqrt86#

The vector projection is

#=-53/86〈-1,9,-2〉#