Let r=(0,0,0)+v(a,b,c) the requested line
There exists a value for v, say and another value, say such that
Let
Solving gives
You can chose one of the coordinates a, b or c
If you chose a = 17 then b = -15 and c = -20
Find a vector equation for the line through the origin that intersects both of the lines r=(2,-16,19)+t(1,1,-4) and r=(14,19,-2)+u(-2,1,2).
This is my work so far, but I can't seem to find the correct answer.
d1=(1,1,-4)
d2=(-2,1,2)
i'm stuck here..
As I said before you can chose any value for a
I have chosen a=17 because it makes the other values very simple
The coordinates of the intersect with r=(2,-16,19)+t(1,1,-4) is given for t=121/16, therefore (153/16,-135/16,-180/16)
If you chose a=17, you will get b=-15, c=-20 and v1=9/16
But if you chose a=34, you will get b=-30, c=-40 and v1=9/32
This does not change the coordinates of the intersect (v1a,v1b,v1c) and does not change either the line since r=(0,0,0)+v(17,-15,-20) and r=(0,0,0)+v(34,-30,-40) are the same line