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.

Alonzo Odom 2022-07-22 Answered
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.
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Answers (2)

gutsy8v
Answered 2022-07-23 Author has 14 answers
Calculating the dot product we get
p q = 5 m 2 + 10 m n 4 m n 8 n 2 = 0
We get
m n = 1 2
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Lillie Pittman
Answered 2022-07-24 Author has 4 answers
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.
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