What is the projection of #<-5,3,7 ># onto #<0,8,-2 >#?

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Answer 1 · 2016-11-26T06:18:41

The projection is #=〈0,20/17,-5/17〉#

Let #veca=〈0,8,-2〉#

and #vecb=〈-5,3,7〉#

The projection of #vecb# onto #veca# is

#=(veca.vecb)/(∥veca∥^2)veca#

Let's calculate the dot product

#veca.vecb=〈0,8,-2〉.〈-5,3,7〉=0*-5+8*3*-2*7=0+24-14=10#

Then, we calculate the modulus of #veca#

#∥veca∥=∥〈0,8,-2〉∥=sqrt(0+64+4)=sqrt68#

The ptojection is #=10/68〈0,8,-2〉=5/34〈0,8,-2〉#

#=〈0,40/34,-10/34〉#

#=〈0,20/17,-5/17〉#