Find angle between u and v (vectors)

[maiia]

1. I've been trying to make sense of what to use in order to solve this any advice?
   
   For the vectors u and v with magnitudes u = 4 and v = 5, find the angle θ between u and v which makes proju v = 3
   

 

[Deleted member 4993]

1. I've been trying to make sense of what to use in order to solve this any advice?
   
   For the vectors u and v with magnitudes u = 4 and v = 5, find the angle θ between u and v which makes proju v = 3

What does proj u v mean:

Projection of vector u onto vector v

or

Projection of vector v onto vector u

Then draw two vectors (u and v) with angle Θ between them - and draw the projection,

Then think .......

If you still cannot get it comeback and tell us how far you did go.

 

[pka]

1. For the vectors u and v with magnitudes u = 4 and v = 5, find the angle θ between u and v which makes proju v = 3

First, let's agree on notation: \(\displaystyle proj_{\vec u}(\vec v) = \dfrac{{\vec v \cdot \vec u}}{{\vec u \cdot \vec u}}\vec u\) AND \(\displaystyle \|\vec{u}\|^2=\vec u \cdot \vec u\)

From the given we get: \(\displaystyle {\vec u \cdot \vec u}=4\). We can get \(\displaystyle {\vec v \cdot \vec u}\) from the \(\displaystyle proj_{\vec u}(\vec v)\).

But note that we can never find the actual vector \(\displaystyle \vec u\).

 

[Ishuda]

1. I've been trying to make sense of what to use in order to solve this any advice?
   
   For the vectors u and v with magnitudes u = 4 and v = 5, find the angle θ between u and v which makes proju v = 3

I think we need to get our notation straight. As I remember it, a projection of one vector onto another is another vector (as indicated by pka) so one can't have the projection of u onto v as the scalar 3 as given in the problem. However, one can talk about the component of u in the v direction which is a scalar and that part of pka's formula given by
\(\displaystyle comp_{\pmb{u}} \pmb{v}\, =\, \dfrac{\pmb{u} \centerdot \pmb{v}}{|\pmb{u}|}\)