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

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Answer 1 · 2016-10-27T17:55:40

The projection is #〈11/27,55/27,99/27〉#

Let #vecb=〈-6,1,5〉# and #veca=〈1,5,9〉#

Then, the vector projection of #vecb# onto #veca# is given by

#(veca.vecb)/(∣veca∣∣veca∣)*veca#

#veca.vecb# is the dot product
and #∣veca∣# is the modulus of the vector

the dot product is #veca.vecb=〈1,5,9〉.〈-6,1,5〉=-6+5+45=44#

#∣veca∣= sqrt(1^2+5^2+9^2)=sqrt(1+25+82)=sqrt108#

so the projection #=(44/108)〈1,5,9〉=(11/27)〈1,5,9〉=〈11/27,55/27,99/27〉#