How do you find the projection of u onto v given #u=<-3, -2># and #v=<-4, -1>#?

1 Answer
Narad T.
Oct 30, 2016

THe projection is #=〈-56/17,-14/17〉#

Explanation:

The vector projection is #=(vecu.vecv)vecv/(∣vecv∣∣vecv∣)#
The dot product is #vecu.vecv=〈u_1,u_2〉〈v_1,v_2〉#
#=u_1v_1+u_2v_2#
Here we have #vecu.vecv=12+2=14#

#∣vecv∣=sqrt(v_1^2+v_2^2)=sqrt(16+1)=sqrt17#

So the vector projection is #=(14/17)〈-4,-1〉=〈-56/17,-14/17〉#

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