Calculating Sin of Angle Between Two Vectors in 3D Space

[touqra]

For two arbitrary vectors in 3D space, subtending an angle, $$\gamma$$ , I know the cos relationship, but what's the sin relationship ? I ask because there is an ambiguity by only knowing the cosine form, since vector A can be either above or below vector B.

$$cos\gamma = cos\theta_1 cos\theta_2 + sin\theta_1 sin\theta_2 cos( \phi_1 - \phi_2 )$$

Sorry I ask a stupid question in this forum, but I didn't know what's the correct term I should type in the search engine to search in the internet.

 

[Mark44]

I'm not sure I understand your question. Is there some reason you need to know which vector is above or below which? If you know the cosine of the angle between the two vectors--which you can get using the dot product: cos(gamma) = (A dot B)/(|A|*|B|)--the sign of cos(gamma) tells you whether gamma is in QI/QIV (cosine > 0) or in QII/QIII (cosine < 0).

I'm not familiar with your formula. What do theta1, theta2, phi1, and phi2 represent?