Question

Given the following points A(1, 0, 1), B(4, 2, 3) and C(0, 2, 0), find the symmetric form of the equation of the line passing through B and C.
I am not sure how to do this and I need help.

Answer 1

You want a set of equations of the form

(x-4)/a = (y-2)/b = (z-3)/c
so, using C,
(0-4)/a = (2-2)/b = (0-3)/c
Now we have a problem, since 2-2=0. In other words, the line has to lie in the plane y=2. So, let's get rid of it. Now we have
(0-4)/a = (0-3)/c
This is satisfied if we use
(0-4)/4 = (0-3)/3
So our line is
(x-4)/4 = (z-3)/3, y=2
This is like
x = 4 - 4t
z = 3 - 3t
Now eliminate t.