I need to find the angle between two unit vectors m → and n → if the vectors p → = m → + 2 n → and q → = 5 m → − 4 n → are perpendicular to each other.

Question

I need to find the angle between two unit vectors       m    →   and       n    →   if the vectors       p    →    =      m    →    +  2      n    →   and       q    →    =  5      m    →    −  4      n    →   are perpendicular to each other.

gutsy8v · Accepted Answer

Calculating the dot product we get            p      →        ⋅            q      →        =  5                    m        →              2    +  10            m      →        ⋅            n      →        −  4            m      →        ⋅            n      →        −  8                    n        →              2    =  0We get            m      →        ⋅            n      →        =      1    2

Lillie Pittman · Accepted Answer

Since p,q are perpendicular and m,n have unit length,  0  =  ⟨  p  ,  q  ⟩  =  ⟨  m  +  2  n  ,  5  m  −  4  n  ⟩  =  5      |    m            |        2    −  4  ⟨  m  ,  n  ⟩  +  10  ⟨  n  ,  m  ⟩  −  8      |    n            |        2    =  −  3  +  6  ⟨  m  ,  n  ⟩  .This, combined with the fact that  cos  ⁡  α  =            ⟨      m      ,      n      ⟩                      |            m              |                    |            n              |              =  ⟨  m  ,  n  ⟩should allow you to find the required angle   α.

Need to find the angle between two unit vectors vec(m) and vec(n) if the vectors vec(p)= vec(m)+2 vec(n) and vec(q)=5 vec(m)−4 vec(n) are perpendicular to each other.

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