if theta is the angle between unit vectors A bar and B bar, then (1-A bar.B bar)/(1 plus A bar.B bar) is equal to
Define u=A.B=ABcosTheta
the problem then is
(1-u)/(1+u)=(1-u)^2/(1-u^2)
To solve this, we'll need to use the dot product of vectors.
The dot product of two vectors A and B is defined as the product of their magnitudes and the cosine of the angle between them:
A · B = |A| |B| cos(theta)
Given that A and B are unit vectors (|A| = |B| = 1), the dot product simplifies to:
A · B = cos(theta)
Substituting this into the expression (1 - A · B) / (1 + A · B), we get:
(1 - cos(theta)) / (1 + cos(theta))
This is the final expression for (1 - A · B) / (1 + A · B) when theta is the angle between unit vectors A and B.