Posted by Shaila on Sunday, September 5, 2010 at 11:26pm.
A line has the same xintercept as
[x,y,z]=[21,8,14]+t[12,4,7] and the same yintercept as
[x,y,z]=[6,8,12]+s[2,5,4]. Write the parametric equation of the line.

Math  equations of lines  Reiny, Sunday, September 5, 2010 at 11:58pm
As I understand it, the xintercept of a line in 3D would be where y=0 and z=0
that is,
[x,0,0] = [21,8,14] + t[12,4,7]
this results in 2 different values of t, thus the line misses the xaxis.
The same would be true for the yintercept of the 2nd line, it would miss the yaxis. 
Math  equations of lines  Shaila, Monday, September 6, 2010 at 12:47pm
Writing the parametric equations of the given line one
x=2112t and since we want the x intercept the y=z=0 therefore
8+4t=0 and 14+7t=0 in both case the t value is '2' repeating the similar procedure to find the yintercept the value of s=3
there after how do i find my parametric equations. 
Math  equations of lines  Reiny, Monday, September 6, 2010 at 1:47pm
You are correct, I made an arithmetic error trying to do it in my head.
ok, so when t = 2
[x,y,z] = [3,0,0] , so the endpoint of that vector is(3,0,0,)
and in the second, when s = 3
[x,y,z] = [0, 7,0] so the endpoint of that vector is (0,7,0)
so the direction vector of the line joining the intercepts is (3,7,0)
and the equation of that line is
[x,y,z] = (3,0,0) + k(3,7,0)