Given two vectors a and b, what is the possible angle between them when ab <= 0?

bucstar11n0h

bucstar11n0h

Answered question

2022-11-17

Angle range when scalar product of vectors less or equal to zero
Given two vectors a and b, what is the possible angle between them when a b 0?

Answer & Explanation

Abril Orr

Abril Orr

Beginner2022-11-18Added 14 answers

Let a and b be two nonzero vectors. I'm going to denote their dot product by a , b . Now, we note that:
a , b = a b cos ( θ )
where θ is the angle between them so that θ [ 0 , π ]. Now, a > 0 and b > 0. So, all we need to do is to observe that:
cos ( θ ) 0
and this is true when θ [ π 2 , π ] . I hope that makes sense

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