Above that of any points straight line in three-dimensional space, it can be represented as a vector r.
It represents a 3D point coordinates as follows:
Let's further understanding through exercises
ex1) Find the vector equation of a line through (-16, 4, 11) and (8, 0, -5)
How to get vector b ?
Let see one more example.
ex2) Find the vector equation of a line through (-7, -7, 2) and parallel to the line in ex1)
vector b is same with ex1), because parallel.
And this line through on (-7, -7, 2), so equation is like that
And let's see one more example.
Don't you interesting?
ex3) Find line equation of vector b.
Firstly, let find AX vector.
And we should get t value.
How? the principles of inner product.
It is a vector perpendicular to the inner product is '0'.
input t value into AX vector. then..
Find the acute angle between line 1 and line 2
In inner product rule,
So, we will follow below formula..