In Linear Algebra, the dimension of a vector space is an important concept. For that you need a basis: a set of vectors that is both linearly independent and spans the space in question. This worksheet gives students the opportunity to practice working with vectors to see if they are independent.
In the Christian faith, the idea of the Trinity, God the Father, God the Son, and God the Holy Spirit, is a difficult one to explain. http://www.bible.ca/trinity/trinity-proof-texts.htm gives some scripture related to the idea of the Trinity. For me the idea of dimension helps here. In space (3 dimensions), 3 different directions are needed to describe the entire (single) space. So the fact that 3 different persons of God are used to describe the one God seems somewhat like needing 3 vectors to describe all of ONE space.
My attempts at integrating faith and discipline are another idea I see relating to linear combinations. I can just do faith statements, I can just do statements about mathematics, but if I can combine them I can communicate more than just faith or mathematics.
Another place where combining topics can be effective is what I have attempted with this whole Faith Illustrations workbook. I have been interested in using interactive figures to explain math concepts for years and that opened up an opportunity to do some work for Pearson on a project: contributing to Thomas' Calculus by Pearson Publishing (see Features given at https://www.pearsonhighered.com/program/Hass-Thomas-Calculus-plus-My-Math-Lab-with-Pearson-e-Text-Access-Card-package-14th-Edition/PGM1248191.html to learn more about the Interactive Figures). I run a camp (see https://sites.google.com/site/sbumathcon/math-contest-camp-2017 ) and I also sing some math songs (see https://www.youtube.com/playlist?list=PLgQhuyBS3_qb65_uFn4dJ-5_tsuQL-vjS for songs I have uploaded to youtube). How can I integrate all my interests so if someone finds me because of one interest, they discover other things I am interested in?