Given u = 1/SQRT(10) (-2,1,-1,2). Find a unit vector v satisfying the condition that u . v = -1.

Answer 1

since u.v = |u||v|cosθ we must have cosθ = -1. In other words,

v = -u

Answer 2

Thanks for that Steve, it makes sense now. Just a follow up question, what kind of geometrical objects that has cosθ = -1?