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

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〉
$= {u}_{1} {v}_{1} + {u}_{2} {v}_{2}$
Here we have $\vec{u} . \vec{v} = 12 + 2 = 14$

∣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〉