Line equation study in 3D

Equations of a straight line in 3D space.

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.

ex4)
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'.
So.

input t value into AX vector. then..

ex5)

Find the acute angle between line 1 and line 2

where 

->

The directions are and   in L1 and L2.

In inner product rule, 

 

So, we will follow below formula..

->