I know the terminology is very weird and probably misled many people form what I’m actually asking, but I don’t know any better way to describe it...
Why is the dot product of $\ b_1 $ and $\ b_2 $ equal to equation below? How did they even get those values?
Can someone guide me through the steps to get the answer?
$\vec b_1 = \vec c_1 \cos \theta + \vec c_2 \sin \theta$
$\vec b_2 = \vec c_2 \cos \theta - \vec c_1 \sin \theta$
$\vec b_1 \cdot \vec b_2 = -(\vec c_1^2 - \vec c_2^2)\sin \theta \cos \theta + \vec c_1 \cdot \vec c_2(\cos^2 \theta - \sin^2 \theta) = 0$
[edit 1] wrote out the equation in MathJax
[edit 2] forgot to mention that $ b_1 $ and $b_2$ are assumed to be perpendicular