Windwaker2004
Nov7-04, 03:04 AM
Hi, I need some help with this question:
Find all values of \ k for which the lines do not intersect.
\ (x-2,y+1,z-3) = (r,0,3r)\ and\ (x,y,z) = (2,1,4)\ +\ s(2,k,6)
I put the first equation in vector form:
\ (x,y,z) = (2,-1,3)\ +\ r(1,0,3)
Now I know that if the direction vectors are scalar multiples of one another, they are parallel lines and therefore do no intersect...
\ d_1 = (1,0,3)\ and\ d_2 = (2,k,6) \ \ d_1 = t(d_2)\ therefore...\ (1,0,3) = t(2,k,6)\ since\ 1 = t2,\ t = 1/2 \ then\ 0 = 1/2(k),\ therefore\ k=0
The second direction vector is a scalar multiple of direction vector 1 at any scalar k?
Find all values of \ k for which the lines do not intersect.
\ (x-2,y+1,z-3) = (r,0,3r)\ and\ (x,y,z) = (2,1,4)\ +\ s(2,k,6)
I put the first equation in vector form:
\ (x,y,z) = (2,-1,3)\ +\ r(1,0,3)
Now I know that if the direction vectors are scalar multiples of one another, they are parallel lines and therefore do no intersect...
\ d_1 = (1,0,3)\ and\ d_2 = (2,k,6) \ \ d_1 = t(d_2)\ therefore...\ (1,0,3) = t(2,k,6)\ since\ 1 = t2,\ t = 1/2 \ then\ 0 = 1/2(k),\ therefore\ k=0
The second direction vector is a scalar multiple of direction vector 1 at any scalar k?