Show that the lines
x=a1s+ b1, y= a2s + b2 , z =a3s+b3 , -infinity<s<infinity
x=c1t+ d1, y= c2t + d2 , z =c3t+d3 , -infinity<t<infinity
intersect or parallel if and only if
| a1 c1 b1-d1 |
| a2 c2 b2-d2 | = 0
| a3 c3 b3-d3 |
I have a start on this problem anyway . . .
Show that the lines: .
. . intersect or are parallel if and only if: .
The lines intersect if: .
. . That is, if the system: . . has a solution
Now we must relate this system to that determinant . . .
[But I truly dislike "if and only if" problems . . . p'too!]