What is the projection of #<2,-5,1 ># onto #<6,-8,3 >#?

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Answer 1 · 2016-12-04T09:34:14

The answer is #=55/109〈6,-8,3〉#

The projection of #vecb# onto #veca# is

#=(veca.vecb)/(∥veca∥^2)veca#

Here, #vecb=〈2,-5,1〉# and #veca=〈6,-8,3〉#

The dot product is

#veca.vecb=〈2,-5,1〉.〈6,-8,3〉=(12+40+3)=55#

The modulus of #veca=∥〈6,-8,3〉∥=sqrt(36+64+9)=sqrt109#

The projection is

#=55/109〈6,-8,3〉#