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

1 Answer
Narad T.
Oct 21, 2016

The vector projection is #〈-31/35,-31/7,93/35〉#

Explanation:

Let #vecb=〈8,-1,6〉#

and #veca=〈-1,5,-3〉#

Then the vector projection of #vecb# onto #veca# is
#=(veca.vecb)/(∣veca∣)^2*veca#
where the dot product is #veca.vecb#

dot product #(8*-1)+(-1*5)+(6*-3) =-8-5-18=-31#

and #(∣veca∣)^2=(1+25+9)=35#

so the projection is #-31/35〈-1,5,-3〉 =〈-31/35,-31/7,93/35〉#

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