Math  equations of lines
posted by Shaila .
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.

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. 
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. 
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)