In this approach, orthogonal vectors are a particular solution of simultaneous linear equations. A plane orthogonal vector is a solution to one linear equation in two unknowns while a spatial orthogonal vector is a particular solution to two linear equations in three unknowns. Also, parallelism is related with the generic solutions and the null vector: the latter is parallel to any vector, while orthogonality is related to particular solutions to simultaneous linear equations.

orthogonal vector, particular solution, parallel, orthogonal.