Problem 635. Angle between Two Vectors
The dot product relationship, a dot b = | a | | b | cos(theta), can be used to determine the acute angle between vector a and vector b ( 0 to pi ).
The definition of | a | is ( a(1)a(1)+a(2)a(2)...+a(n)a(n) )^0.5.
The definition of "a dot b" is a(1)b(1)+a(2)b(2)...+a(n)b(n). (wikipedia)
In 3-D the angle is in the plane created by the vectors a and b.
The input may be a 2-D or a 3-D vector. These represent physical models.
An extension of this angular determination given vectors problem is to provide two points for each vector. The practical application relates to Laser Trackers which best fit multiple points for lines, surfaces, annular surfaces, and other reference points.
Examples:
a=[1 0] (x-axis); b=[0 1] (y-axis) which intersect at 90 degrees (pi/2)
theta=acos(a dot b/(|a||b|)=acos(0/(1*1))=pi/2 radians
a=[1 1 0] 45 degrees in xy plane b=[1 1 1.414] 45 degree vector in Z above a 45 degree rotation in XY plane.
theta=acos(a dot b/(|a||b|)=acos(2/(1.414*2))=pi/4 radians
Solution Stats
Problem Comments
-
1 Comment
Spookily similar to Problem 381 ("Angle between two vectors")....
Solution Comments
Show commentsProblem Recent Solvers349
Suggested Problems
-
97584 Solvers
-
Find relatively common elements in matrix rows
2037 Solvers
-
Flip the main diagonal of a matrix
787 Solvers
-
384 Solvers
-
1334 Solvers
More from this Author308
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!