white differences between 0 and π
Answers
The maximum value of C will be |A|+|B| when angle between A and B will be zero.
The minimum value of C will be |A| - |B| when angle between A and B will be pi.
Thus entire range of values of C is covered by angles from zero to pi between A and B .
Now, cos of angle between A and B being periodic , the values of the angle between pi and 2pi will repeat the value of C which are obtained for angles between zero and pi.
In dot and cross products also we get same kind of result due to the fact that cosine and sine functions are periodic.
Therefore , angle between two vectors lie between 0 and pi.
Why can't an angle between two vectors be greater than 180°?
Why dot product of two vectors is defined for angle between o and 180 degrees?
How do I find a such that the angle between vectors v= (1,a,2) and u= (a,4,4) is pi/4?
If the angle between two vectors is 180 degrees, are the two vectors parallel?
Why do we take a small angle between two vectors instead of a greater angle?
Rule to find angle between two vectors:
Match tails of both vectors and smaller angle is the angle between both vectors and small angle can’t be greater than ‘pi’ and less than ‘zero’
Extremes. Imagine a tombstone. “Here lies anon, who asked a good question on Quora. Born 1998. Died 2098.” A person’s birth day and their death day are the extremes of their life. Obviously a lot happens between those extremes. But the extremes are important enough that we print them on their tombstone! Same thing with vectors. When two vectors point on the same direction, the angle between them is zero, and they add 100%. When two vectors point in completely opposite directions, the angle between them is 180 degrees aka pi, and they cancel 100%. Those are extremes—100% addition or 100% cancellation. So for two vectors, we think about their angle as being at one of these two extremes (0 or pi) or somewhere in between.