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..


->










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