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# FP3 vectors watch

1. so, this question SHOULD be easy - but i just cant do it - gaaah!!

l1: r = i - j + s(i + 2j + 3k)
l2: r = 2i + j + k + t(2i - j + k)

the points A and B lie on l1 and l2 respectively.
the line AB is perpendicular to l1 and l2.

find the coordinates of A and B.

so errr... the direction vector of the line perpendicular to AB is (i + j - k)
and i know there's probably some kind of simultaneous equations i'm meant to be solving, but however i do it, i get about 6 variables, and it just seems too complicated compared to the rest of the exercise.

help much appreciated!!!
thanks.
2. (Original post by rachel123456)
so, this question SHOULD be easy - but i just cant do it - gaaah!!

l1: r = i - j + s(i + 2j + 3k)
l2: r = 2i + j + k + t(2i - j + k)

the points A and B lie on l1 and l2 respectively.
the line AB is perpendicular to l1 and l2.(

find the coordinates of A and B.

so errr... the direction vector of the line perpendicular to AB is (i + j - k)
and i know there's probably some kind of simultaneous equations i'm meant to be solving, but however i do it, i get about 6 variables, and it just seems too complicated compared to the rest of the exercise.

help much appreciated!!!
thanks.
I think what you do is rewrite for l_1

comparing we find the values of

so A has the above position vector ..
similarly find B from l_2
and also we know (B-A)=direction vector(you have already found out) and solve it from there ?
3. lol - i really should have been able to do that myself!

you are a saint - thank you! (it worked wonderfully)

xxx

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