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

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Answer 1 · 2016-12-21T14:41:30

The answer is #=-57/83〈7,-3,-5〉#

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

#=(veca.vecb)/(∥veca∥^2)veca#

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

#=(-7-15-35)=-57#

The modulus of #veca# is #=∥veca∥=∥〈7,-3,-5〉∥#

#=sqrt(49+9+25)=sqrt83#

The vector projection is #=-57/83〈7,-3,-5〉#