What is the projection of #<-2,2,5 ># onto #<1,6,9 >#?

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Answer 1 · 2016-12-19T10:33:58

The answer is #=55/118〈1,6,9〉#

The projection of #vecb# onto #veca# is

#=(veca.vecb)/(∥veca∥^2)veca#

The dot product is #=〈-2,2,5〉.〈1,6,9〉#

#=(-2+12+45)#

#=55#

The modulus of #veca#

#=∥〈1,6,9〉∥#

#=sqrt(1+36+81)=sqrt118#

Therefore,

the projection is

#=55/118〈1,6,9〉#