1. The problem statement, all variables and given/known data I am preparing for my calculus III class over the break. I came across the formula for the angle between two planes which is: cosΘ = (|a.b|)/(||a|||b||) 2. Relevant equations cosΘ = (|a.b|)/(||a|||b||) a.b = ||a||||b||cosΘ 3. The attempt at a solution I know that the dot product formula is: a.b = ||a||||b||cosΘ Why do we put the absolute value bars when we are trying to find the angle between two planes if the original formula doesn't have absolute values in it?