# Thread: Planes and Lines IV

1. ## Planes and Lines IV

Question 4: u, v and w are three vectors in three-dimensional space. |u| = 5, |v| = 2 and |w| = 1. The angle between u and w is π/3. What should the angle between u and v be so that |u + 2v + w| = |u + v + 2w|?

2. ## Re: Planes and Lines IV

$\displaystyle (u+2v+w) \cdot (u+2v+w)=(u+v+2w) \cdot (u+v+2w)$

that's the dot product. expand, simplify, replace