I'm a software engineer with very little real world math experience.
I'm studying computer vision and interested in learning how to calculate the exact distance and position of an object A from an object B within a 3D space.
Can someone please tell me what branch of mathematics I need to learn to solve the above problem? From schooling days - Linear Algebra and Trigonometry come to mind, is this right?
Yes, it is Linear Algebra, which consists of topics about linear transformation (rotation, scaling, etc.) and vector operations. For example, OpenGL uses matrices to do rotation, scaling, and even translation. For example, if we were to calculate distance between two points in an n-dimensional space (pedantically, two vectors $u,v\in\mathbb{R}^n$), we will use the following notation:
$$ \|u-v\|=\sqrt{\sum_{k=1}^n(u_k-v_k)^2} $$
I believe Linear Algebra is the branch of mathematics talking about.