How to derive the equation of a straight line in R3 space through a point and a direction vector through a determinant?

Question

Mathematics

From the conditions: d - direction vector, M0 - given point, M - any point on the line

Answer 1

Via vectors: M = M0 + td, t is a parameter.
(we distinguish between point M0 and vector td, but point + vector = point)
By coordinates: x = x0 + pt, etc.
Let's write down what t equals, and we get our equation.