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Hi, I need some help with this question:

Find all values of [tex] \ k [/tex] for which the lines do not intersect.

[tex] \ (x-2,y+1,z-3) = (r,0,3r)\ and\ (x,y,z) = (2,1,4)\ +\ s(2,k,6) [/tex]

I put the first equation in vector form:

[tex] \ (x,y,z) = (2,-1,3)\ +\ r(1,0,3) [/tex]

Now I know that if the direction vectors are scalar multiples of one another, they are parallel lines and therefore do no intersect...

[tex] \ 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 [/tex]

The second direction vector is a scalar multiple of direction vector 1 at any scalar k?

Find all values of [tex] \ k [/tex] for which the lines do not intersect.

[tex] \ (x-2,y+1,z-3) = (r,0,3r)\ and\ (x,y,z) = (2,1,4)\ +\ s(2,k,6) [/tex]

I put the first equation in vector form:

[tex] \ (x,y,z) = (2,-1,3)\ +\ r(1,0,3) [/tex]

Now I know that if the direction vectors are scalar multiples of one another, they are parallel lines and therefore do no intersect...

[tex] \ 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 [/tex]

The second direction vector is a scalar multiple of direction vector 1 at any scalar k?

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